Illustrative Math Alignment: Grade 7 Unit 7
Angles, Triangles, and Prisms
Lesson 1: Relationships of Angles
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Geometric Shapes--Congruent Triangles--Example 6 | Math Example--Geometric Shapes--Congruent Triangles--Example 6TopicGeometry DescriptionThe image displays two triangles. The left triangle is labeled ABC. The right triangle is labeled DEF. We are given congruent corresponding sides and angles. Using the SAS Postulate, the two triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides. |
Definition of a Triangle |
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Math Example--Geometric Shapes--Congruent Triangles--Example 7 | Math Example--Geometric Shapes--Congruent Triangles--Example 7TopicGeometry DescriptionThe image shows two triangles. The left triangle is labeled ABC . The right triangle is labeled DEF. We are given pairs of corresponding angles and corresponding sides. Using the AAS Postulate, we can prove the triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides. |
Definition of a Triangle |
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Math Example--Geometric Shapes--Congruent Triangles--Example 8 | Math Example--Geometric Shapes--Congruent Triangles--Example 8TopicGeometry DescriptionThe image depicts two triangles. The left triangle is labeled ABC. The right triangle is labeled DEF. We are given pairs of corresponding angles and a pair of corresponding sides. Using the ASA Postulate, the two triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides. |
Definition of a Triangle |
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Math Example--Geometric Transformation--Translating Triangles--Example 1 | Math Example--Geometric Transformation--Translating Triangles--Example 1TopicTransformations DescriptionA triangle on a grid is translated 4 units to the left. It shows the original triangle ABC and the translated triangle A'B'C'. Example 1: "Draw the triangle that results from the following translation: 4 units to the left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 10 | Math Example--Geometric Transformation--Translating Triangles--Example 10TopicTransformations Description
The triangle is translated 4 units to the left and 2 units up. It displays both the initial and the translated triangles. Example 10: "Draw the triangle that results from the following translation: 4 units to the left, 2 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 11 | Math Example--Geometric Transformation--Translating Triangles--Example 11TopicTransformations DescriptionTriangle ABC is translated horizontally to the right by 4 units to form triangle A'B'C'. Example 11: The translation is described as 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 12 | Math Example--Geometric Transformation--Translating Triangles--Example 12TopicTransformations DescriptionTriangle ABC is translated vertically downward by 6 units to form triangle A'B'C'. Example 12: The translation is described as 6 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 13 | Math Example--Geometric Transformation--Translating Triangles--Example 13TopicTransformations DescriptionTriangle ABC is translated horizontally to the left by 5 units to form triangle A'B'C'. Example 13: The translation is described as 5 units to the left. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 14 | Math Example--Geometric Transformation--Translating Triangles--Example 14TopicTransformations DescriptionTriangle ABC is translated vertically upward by 6 units to form triangle A'B'C'. Example 14: The translation is described as 6 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 15 | Math Example--Geometric Transformation--Translating Triangles--Example 15TopicTransformations Description
Triangle ABC is translated diagonally 5 units to the right and 5 units downward to form triangle A'B'C'. Example 15: The translation is described as 5 units to the right and 5 units down. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 16 | Math Example--Geometric Transformation--Translating Triangles--Example 16TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units to the right and 3 units upward to form triangle A'B'C'. Example 16: The translation is described as 4 units to the right and 3 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 17 | Math Example--Geometric Transformation--Translating Triangles--Example 17TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units downward and 4 units to the right to form triangle A'B'C'. Example 17: The translation is described as 4 units down and 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 18 | Math Example--Geometric Transformation--Translating Triangles--Example 18TopicTransformations Description
Triangle ABC is translated diagonally 3 units upward and 3 units to the right to form triangle A'B'C'. Example 18: The translation is described as 3 units up and 3 units to the right. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 19 | Math Example--Geometric Transformation--Translating Triangles--Example 19TopicTransformations DescriptionTriangle ABC is translated diagonally 6 units to the left and 4 units downward to form triangle A'B'C'. Example 19: The translation is described as 6 units to the left and 4 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 2 | Math Example--Geometric Transformation--Translating Triangles--Example 2TopicTransformations DescriptionA triangle on a grid is translated 5 units to the right. The diagram shows the original triangle ABC and the new position, A'B'C'.. Example 2: "Draw the triangle that results from the following translation: 5 units to the right." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 20 | Math Example--Geometric Transformation--Translating Triangles--Example 20TopicTransformations DescriptionTriangle ABC is translated diagonally 2 units to the left and 5 units upward to form triangle A'B'C'. Example 20: The translation is described as 2 units to the left and 5 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 21 | Math Example--Geometric Transformation--Translating Triangles--Example 21TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 22 | Math Example--Geometric Transformation--Translating Triangles--Example 22TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 3 | Math Example--Geometric Transformation--Translating Triangles--Example 3TopicTransformations DescriptionA triangle on a grid is translated 4 units up. The figure displays both the original and translated triangles ABC and A'B'C'.. Example 3: "Draw the triangle that results from the following translation: 4 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 4 | Math Example--Geometric Transformation--Translating Triangles--Example 4TopicTransformations DescriptionA triangle on a grid is translated 5 units down. It shows the original triangle and its new position after translation, labeled A'B'C'. Example 4: "Draw the triangle that results from the following translation: 5 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 5 | Math Example--Geometric Transformation--Translating Triangles--Example 5TopicTransformations DescriptionA triangle is translated 4 units to the left and 2 units down. Both the original and the new triangles, ABC and A'B'C', are illustrated. Example 5: "Draw the triangle that results from the following translation: 4 units to the left, 2 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 6 | Math Example--Geometric Transformation--Translating Triangles--Example 6TopicTransformations DescriptionThe triangle is translated 5 units to the right and 3 units up. The image includes both original and translated triangles, labeled ABC and A'B'C'. Example 6: "Draw the triangle that results from the following translation: 5 units to the right, 3 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 7 | Math Example--Geometric Transformation--Translating Triangles--Example 7TopicTransformations DescriptionA triangle is translated 4 units up and 5 units left, showing the original ABC and translated A'B'C' triangles. Example 7: "Draw the triangle that results from the following translation: 4 units up, 5 units left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 8 | Math Example--Geometric Transformation--Translating Triangles--Example 8TopicTransformations Description
The triangle is translated 5 units up and 2 units right. The image shows both the original and translated positions of the triangle. Example 8: "Draw the triangle that results from the following translation: 5 units up, 2 units rogjt." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 9 | Math Example--Geometric Transformation--Translating Triangles--Example 9TopicTransformations DescriptionA triangle is translated 4 units to the right and 3 units down. The image shows both the original and the new triangle positions. Example 9: "Draw the triangle that results from the following translation: 4 units to the right, 3 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Numbers--Partitioning Rectangles: Example 1 | Math Example--Numbers--Partitioning Rectangles: Example 1
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 2 | Math Example--Numbers--Partitioning Rectangles: Example 2
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 3 | Math Example--Numbers--Partitioning Rectangles: Example 3
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 4 | Math Example--Numbers--Partitioning Rectangles: Example 4
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 5 | Math Example--Numbers--Partitioning Rectangles: Example 5
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 6 | Math Example--Numbers--Partitioning Rectangles: Example 6
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 7 | Math Example--Numbers--Partitioning Rectangles: Example 7
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Numbers--Partitioning Rectangles: Example 8 | Math Example--Numbers--Partitioning Rectangles: Example 8
This is part of a collection of math examples that focus on numbers and their properties. |
Identifying Shapes and Counting |
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Math Example--Polygons--Quadrilateral Classification: Example 1 | Math Example--Polygons--Quadrilateral Classification: Example 1TopicGeometry DescriptionThis example presents a quadrilateral with labeled sides: AB = 5, BC = 4, CD = 3, and DA = 6. The task is to classify the quadrilateral based on these measurements. Since none of the sides are congruent and no specific relationships among the sides can be determined, this shape is classified as a generic quadrilateral. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 10 | Math Example--Polygons--Quadrilateral Classification: Example 10TopicGeometry DescriptionThis example showcases a quadrilateral with right angles labeled with variable x at two corners, labeled as A, B, C, and D. To classify this shape, we need to solve for x: 90 + 90 + 2x = 360, which gives us x = 90. This means all angles are 90 degrees. Since opposite sides are parallel and congruent, we can classify this shape as a rectangle. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 11 | Math Example--Polygons--Quadrilateral Classification: Example 11TopicGeometry DescriptionThis example presents a square with all sides congruent and right angles, labeled as A, B, C, and D. The task is to classify the quadrilateral based on these characteristics. As all interior angles are 90 degrees and all sides are congruent, this shape is confirmed to be a square. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 12 | Math Example--Polygons--Quadrilateral Classification: Example 12TopicGeometry DescriptionThis example features a quadrilateral with all sides labeled x and marked congruent, labeled as A, B, C, and D. To classify this shape, we need to solve for x: 4x = 360, which gives us x = 90. This means all angles are 90 degrees. Since all sides are congruent and all angles are right angles, we can classify this shape as a square. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 13 | Math Example--Polygons--Quadrilateral Classification: Example 13TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with all sides marked as congruent and angles marked as right angles. The side lengths are indicated with x. To classify this shape, we solve for x: 90 + 90 + 2x = 360, which gives us x = 90. This confirms that all interior angles are 90 degrees. Since all sides are congruent and all angles are right angles, we can classify this shape as a square. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 14 | Math Example--Polygons--Quadrilateral Classification: Example 14TopicGeometry DescriptionThis example showcases a quadrilateral labeled ABCD with all sides marked as congruent and angles marked as right angles. Each side is labeled with a length of 1. Based on these characteristics, we can classify this shape as a square. All sides are congruent, which means opposite sides are parallel. Angle ABC is 90 degrees, and its adjacent angles are supplementary, confirming that all interior angles are 90 degrees. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 15 | Math Example--Polygons--Quadrilateral Classification: Example 15TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with all sides marked as congruent and angles marked as right angles. The side lengths are indicated with x. Based on these characteristics, we can classify this shape as a square. Because all sides are congruent, opposite sides are parallel. Angle ABC is 90 degrees, and its adjacent angles are supplementary, confirming that all interior angles are 90 degrees. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 16 | Math Example--Polygons--Quadrilateral Classification: Example 16TopicGeometry DescriptionThis example features a quadrilateral labeled ABCD with two sides labeled with lengths of 5 and x, and angles marked as right angles. The diagram shows perpendicular lines and parallel lines. Based on these characteristics, we can classify this shape as a square. Because angle ABC and angle BAD are supplementary, BC and AD are parallel. Since AB and CD are congruent, angle BAD and angle ADC are supplementary. Therefore, all interior angles are 90 degrees, and all sides are congruent. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 17 | Math Example--Polygons--Quadrilateral Classification: Example 17TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with all sides marked as 5 units, indicating congruence. Based on this characteristic, we can classify this shape as a rhombus. The key property that defines a rhombus is that all sides are congruent, which is clearly demonstrated in this example. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 18 | Math Example--Polygons--Quadrilateral Classification: Example 18TopicGeometry DescriptionThis example showcases a quadrilateral labeled ABCD with all sides marked as x, indicating congruence. Based on this characteristic, we can classify this shape as a rhombus. The defining property of a rhombus is that all sides are congruent, which is clearly demonstrated in this example by using the variable x for all side lengths. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 19 | Math Example--Polygons--Quadrilateral Classification: Example 19TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with sides AB and CD marked as x, and BC and AD marked as 5. Opposite sides are noted to be parallel. Based on these characteristics, we can classify this shape as a rhombus. The key properties that define this as a rhombus are: opposite sides are parallel, and opposite sides are congruent. Since x = 5, all sides are congruent, which is a defining property of a rhombus. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 2 | Math Example--Polygons--Quadrilateral Classification: Example 2TopicGeometry DescriptionThis example showcases a quadrilateral with sides labeled as variables: x, y, z, and w. The task is to classify the quadrilateral based on this information. As no specific relationships between the sides are given, and no sides are stated to be congruent, this shape is classified as a generic quadrilateral. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 20 | Math Example--Polygons--Quadrilateral Classification: Example 20TopicGeometry DescriptionThis example features a quadrilateral labeled ABCD with angles B and D marked as 120 degrees, and angles A and C as 60 degrees. Sides AB and BC are marked as congruent. Based on these characteristics, we can classify this shape as a rhombus. All pairs of adjacent angles are supplementary (120° + 60° = 180°), which means opposite sides are parallel. Since AB is congruent to BC, and opposite sides are congruent in a parallelogram, all sides must be congruent, defining this shape as a rhombus. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 21 | Math Example--Polygons--Quadrilateral Classification: Example 21TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with sides marked as x and y. The opposite sides are noted to be congruent, and there's an additional note indicating AB is congruent to BC. Based on these characteristics, we can classify this shape as a rhombus. Both pairs of opposite angles are congruent, which means opposite sides are parallel. Since AB is congruent to BC, and opposite sides are congruent, all sides must be congruent, defining this shape as a rhombus. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 22 | Math Example--Polygons--Quadrilateral Classification: Example 22TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with angles marked as 70° and sides marked as x. Opposite angles are noted to be congruent, and there's an additional note indicating AB is congruent to BC. Based on these characteristics, we can classify this shape as a rhombus. Both pairs of opposite angles are congruent, which means opposite sides are parallel. Since AB is congruent to BC, and opposite sides are congruent in a parallelogram, all sides must be congruent, defining this shape as a rhombus. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 23 | Math Example--Polygons--Quadrilateral Classification: Example 23TopicGeometry DescriptionThis example features a quadrilateral labeled ABCD with angles marked as 120° and 80°. Opposite angles are noted to be congruent. Based on these characteristics, we can classify this shape as a parallelogram. Both pairs of opposite angles are congruent, which means opposite sides are parallel, a defining property of parallelograms. |
Definition of a Quadrilateral |
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Math Example--Polygons--Quadrilateral Classification: Example 24 | Math Example--Polygons--Quadrilateral Classification: Example 24TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with sides marked as x and y. The opposite sides are noted to be congruent. Based on these characteristics, we can classify this shape as a parallelogram. Both pairs of opposite sides are congruent, which means opposite sides are parallel, a defining property of parallelograms. |
Definition of a Quadrilateral |
