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.
| Thumbnail Image | Title | Body | Curriculum Nodes |
|---|---|---|---|
|
Math Example--Polygons--Quadrilateral Classification: Example 25 | Math Example--Polygons--Quadrilateral Classification: Example 25TopicGeometry DescriptionThis example showcases a quadrilateral labeled ABCD with angles at B and D marked as 60 degrees. Sides AD and BC are labeled y. The shape is identified as a parallelogram. This classification is based on the fact that both pairs of opposite angles are congruent, which means opposite sides are parallel, a defining property of parallelograms. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 26 | Math Example--Polygons--Quadrilateral Classification: Example 26TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with sides AB and CD measuring 10, and sides BC and AD measuring 12. The shape is identified as a parallelogram. This classification is based on the fact that opposite sides are congruent, which means that opposite sides are parallel, a defining property of parallelograms. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 27 | Math Example--Polygons--Quadrilateral Classification: Example 27TopicGeometry DescriptionThis example features a quadrilateral labeled ABCD with sides AB and CD labeled y, and sides AD and BC labeled x. The shape is identified as a parallelogram. This classification is based on the fact that opposite sides are congruent, which means that opposite sides are parallel, a defining property of parallelograms. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 28 | Math Example--Polygons--Quadrilateral Classification: Example 28TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with sides BC and AD parallel, and AB and CD parallel. Side BC is marked as 5, and side AD is marked as x. Based on these characteristics, we can classify this shape as a parallelogram. Opposite sides are parallel (BC // AD, AB // CD), which is the defining property of a parallelogram. However, adjacent sides are not necessarily congruent, as BC is 5 and AD is x. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 29 | Math Example--Polygons--Quadrilateral Classification: Example 29TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with angles marked as 110°, 100°, 70°, and 80°. Two pairs of adjacent angles are supplementary. Based on these characteristics, we can classify this shape as a trapezoid. The key property that defines this as a trapezoid is that two pairs of adjacent angles are supplementary, which means that BC and AD are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 3 | Math Example--Polygons--Quadrilateral Classification: Example 3TopicGeometry DescriptionThis example presents a quadrilateral with labeled angles: A = 60°, B = 80°, C = 120°, and D = 100°. The task is to classify the quadrilateral based on these angle measurements. Since no pair of adjacent angles is supplementary (adds up to 180°), none of the opposite sides are parallel. As a result, this shape is classified as a generic quadrilateral. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 30 | Math Example--Polygons--Quadrilateral Classification: Example 30TopicGeometry DescriptionThis example features a quadrilateral labeled ABCD with angles marked as w, x, y, and z. It states that w + y = 180° and x + z = 180°. Based on these characteristics, we can classify this shape as a trapezoid. The key property that defines this as a trapezoid is that two pairs of adjacent angles are supplementary, which means that BC and AD are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 31 | Math Example--Polygons--Quadrilateral Classification: Example 31TopicGeometry DescriptionThis example presents a quadrilateral labeled ABCD with angles ABC = 95° and BAD = 85°. It states that angles x and z are also supplementary due to two pairs of adjacent angles being supplementary. Based on these characteristics, we can classify this shape as a trapezoid. The key property that defines this as a trapezoid is that two pairs of adjacent angles are supplementary, which means that BC and AD are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 32 | Math Example--Polygons--Quadrilateral Classification: Example 32TopicGeometry DescriptionThis example showcases a trapezoid with vertices labeled A, B, C, D. The side lengths are given as AB = 10, BC = 7, CD = 9, and AD = 12. It is stated that BC and AD are parallel. Based on these characteristics, we can confirm that this shape is indeed a trapezoid. The key property that defines this as a trapezoid is that one pair of opposite sides (BC and AD) are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 33 | Math Example--Polygons--Quadrilateral Classification: Example 33TopicGeometry DescriptionThis example presents a trapezoid with vertices labeled A, B, C, D. The sides are labeled as w, x, y, and z. It is stated that BC and AD are parallel. Based on these characteristics, we can confirm that this shape is indeed a trapezoid. The key property that defines this as a trapezoid is that one pair of opposite sides (BC and AD) are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 34 | Math Example--Polygons--Quadrilateral Classification: Example 34TopicGeometry DescriptionThis example features a trapezoid with vertices labeled A, B, C, D. The side lengths are given as AB = 15, BC = x, CD = z, and AD = 18. It is stated that BC and AD are parallel. Based on these characteristics, we can confirm that this shape is indeed a trapezoid. The key property that defines this as a trapezoid is that one pair of opposite sides (BC and AD) are parallel. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 4 | Math Example--Polygons--Quadrilateral Classification: Example 4TopicGeometry DescriptionThis example features a quadrilateral with angles 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 angles are given, and no angles are stated to be congruent or supplementary, this shape is classified as a generic quadrilateral. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 5 | Math Example--Polygons--Quadrilateral Classification: Example 5TopicGeometry DescriptionThis example presents a quadrilateral with no right angles or congruent sides, labeled with angles and side lengths. The task is to classify the quadrilateral based on these characteristics. Since no adjacent angles are supplementary and no sides are parallel, this shape is classified as a generic quadrilateral. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 6 | Math Example--Polygons--Quadrilateral Classification: Example 6TopicGeometry DescriptionThis example showcases a rectangle with opposite sides labeled as 3 and 1, and all angles are right angles. The task is to classify the quadrilateral based on these characteristics. As the shape has opposite sides that are congruent and all interior angles are 90 degrees, it is identified as a rectangle. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 7 | Math Example--Polygons--Quadrilateral Classification: Example 7TopicGeometry DescriptionThis example presents a rectangle with opposite sides labeled x and y, and all angles are right angles. The task is to classify the quadrilateral based on these characteristics. Due to the congruent opposite sides and all interior angles being 90 degrees, this shape is identified as a rectangle. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 8 | Math Example--Polygons--Quadrilateral Classification: Example 8TopicGeometry DescriptionThis example features a rectangle with sides labeled 7 and 5, and all angles are right angles. The task is to classify the quadrilateral based on these characteristics. As all interior angles are 90 degrees and opposite sides are parallel and congruent, this shape is confirmed to be a rectangle. |
Definition of a Quadrilateral |
|
Math Example--Polygons--Quadrilateral Classification: Example 9 | Math Example--Polygons--Quadrilateral Classification: Example 9TopicGeometry DescriptionThis example presents a quadrilateral with all right angles, labeled as A, B, C, and D. The opposite sides are parallel and congruent. Based on these characteristics, the shape is classified as a rectangle. All interior angles are 90 degrees, and the opposite sides are both parallel and congruent, which are defining properties of a rectangle. |
Definition of a Quadrilateral |
|
Math Example--Right Triangles-- Example 1 | Math Example--Right Triangles-- Example 1TopicRight Triangles DescriptionThis example presents a right triangle with sides of length 8 and 10, and an unknown hypotenuse labeled c. The task is to find the value of c using the Pythagorean Theorem. By applying the formula a2 + b2 = c2, we can calculate that c = √(102 + 82) = √(164) = 2 * √(41). |
Right Triangles |
|
Math Example--Right Triangles-- Example 10 | Math Example--Right Triangles-- Example 10TopicRight Triangles |
Right Triangles |
|
|
Math Example--Right Triangles-- Example 11 | Math Example--Right Triangles-- Example 11TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 12 | Math Example--Right Triangles-- Example 12TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 13 | Math Example--Right Triangles-- Example 13TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 14 | Math Example--Right Triangles-- Example 14TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 15 | Math Example--Right Triangles-- Example 15TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 16 | Math Example--Right Triangles-- Example 16TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 17 | Math Example--Right Triangles-- Example 17TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 18 | Math Example--Right Triangles-- Example 18TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 19 | Math Example--Right Triangles-- Example 19TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 2 | Math Example--Right Triangles-- Example 2TopicRight Triangles DescriptionIn this example, we have a right triangle with sides of length 3 and 4, and an unknown hypotenuse labeled c. The goal is to determine the value of c using the Pythagorean Theorem. By applying the formula a2 + b2 = c2, we can calculate that c = √(32 + 42) = √(25) = 5. This example builds upon the previous one, reinforcing the application of the Pythagorean Theorem in right triangles. It demonstrates how the theorem can be used with different side lengths, helping students understand its versatility in solving various right triangle problems. |
Right Triangles |
|
Math Example--Right Triangles-- Example 20 | Math Example--Right Triangles-- Example 20TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 21 | Math Example--Right Triangles-- Example 21TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 22 | Math Example--Right Triangles-- Example 22TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 23 | Math Example--Right Triangles-- Example 23TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 24 | Math Example--Right Triangles-- Example 24TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 25 | Math Example--Right Triangles-- Example 25TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 26 | Math Example--Right Triangles-- Example 26TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 3 | Math Example--Right Triangles-- Example 3TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 4 | Math Example--Right Triangles-- Example 4TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 5 | Math Example--Right Triangles-- Example 5TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 6 | Math Example--Right Triangles-- Example 6TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 7 | Math Example--Right Triangles-- Example 7TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 8 | Math Example--Right Triangles-- Example 8TopicRight Triangles |
Right Triangles |
|
Math Example--Right Triangles-- Example 9 | Math Example--Right Triangles-- Example 9TopicRight Triangles |
Right Triangles |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 1 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 1TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 10 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 10TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 2 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 2TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 3 | TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 4 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 4TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 5 | TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
|
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 6 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 6TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
