Illustrative Math Alignment: Grade 8 Unit 2

Topic

Geometry Concepts

Description

This image depicts a kite shape, characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite shape. How do its symmetrical properties and intersecting diagonals help us understand its geometry? What are some mathematical concepts you can explore using kite shapes?"

Topic

Geometry Concepts

Description

This image illustrates a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Topic

Geometry Concepts

Description

This image illustrates a triangular-shaped kite. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is this a kite in the everyday sense? Is this a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image features a triangular-shaped kite. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Examine this kite. How is it a kite in the everyday sense? Is it geometrically a kite?"

Topic

Geometry Concepts

Description

This image depicts a triangular-shaped kite. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is this a kite in the everyday sense? Is this a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a triangular-shaped kite. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is this a kite in the everyday sense? Is this a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image depicts another variation of a kite shape, in this case a circular shape. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is it a kite in the everyday sense? Is it a kite in a geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a circular kite shape. Geometrically, a kite is a a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is a kite in the everyday sense of the word? Is it a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image features a hexagonal kite shape. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Examine this kite. How is it a kite in the everyday sense? Is it a kite in a geometric sense?"

Topic

Geometry Concepts

Description

This image depicts a hexagonal kite shape. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is this a kite in the everydays sense of the word? Is it a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a hexagonal kite shape. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is it a kite in the everyday sense? Is it a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image features a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Topic

Geometry Concepts

Description

This image depicts a kite shape, characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite shape. How do its symmetrical properties and intersecting diagonals help us understand its geometry? What are some mathematical concepts you can explore using kite shapes?"

Topic

Geometry Concepts

Description

This image illustrates a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Topic

Geometry Concepts

Description

This image illustrates two hexagons: one regular and one irregular. A hexagon is a six-sided polygon. In a regular hexagon, all sides and angles are equal, with each interior angle measuring 120 degrees. This symmetry gives it a balanced and uniform appearance.

An irregular hexagon, by contrast, has sides and angles that are not all equal. This lack of uniformity means that the hexagon can take on a variety of shapes, depending on the specific lengths and angles of its sides.

Topic

Geometry Concepts

Description

This image shows two octagons: one regular and one irregular. An octagon is an eight-sided polygon. In a regular octagon, all sides and angles are equal, with each interior angle measuring 135 degrees. This regularity gives it a symmetrical and balanced appearance.

An irregular octagon, on the other hand, has sides and angles that are not all equal. This asymmetry means that the octagon can have a variety of shapes, depending on the specific lengths and angles of its sides.

Topic

Geometry Concepts

Description

This image depicts two pentagons: one regular and one irregular. A pentagon is a five-sided polygon. In a regular pentagon, all sides and angles are equal, with each interior angle measuring 108 degrees. This regularity gives it a symmetrical and balanced appearance.

An irregular pentagon, however, has sides and angles that are not all equal. This asymmetry allows the pentagon to take on various shapes, depending on the specific lengths and angles of its sides.

Topic

Geometry Concepts

Description

This image illustrates two quadrilaterals: one regular and one irregular. A quadrilateral is a four-sided polygon. In a regular quadrilateral, such as a square, all sides and angles are equal, with each interior angle measuring 90 degrees. This regularity gives it a symmetrical and balanced appearance.

An irregular quadrilateral, however, has sides and angles that are not all equal. This asymmetry allows the quadrilateral to take on various shapes, depending on the specific lengths and angles of its sides.

Topic

Geometry Concepts

Description

This image shows two triangles: one regular and one irregular. A triangle is a three-sided polygon. In a regular triangle, also known as an equilateral triangle, all sides and angles are equal, with each interior angle measuring 60 degrees. This regularity gives it a symmetrical and balanced appearance.

An irregular triangle, however, has sides and angles that are not all equal. This asymmetry allows the triangle to take on various shapes, depending on the specific lengths and angles of its sides.

Topic

Geometry Concepts

Description

This image depicts a square undergoing a dilation transformation. Dilation changes the size of a figure while maintaining its shape, resulting in a similar figure. The scale factor of the dilation determines whether the square is enlarged or reduced.

In this transformation, all sides of the square are scaled by the same factor, and all angles remain congruent to the original. This preserves the square's shape while changing its size, demonstrating the concept of similarity in geometry.

Topic

Geometry Concepts

Description

This image shows a square undergoing a combination of dilation and translation. The dilation changes the size of the square while maintaining its shape, and the translation moves the dilated square to a new position without changing its size or orientation.

This composite transformation demonstrates how multiple transformations can be applied sequentially. The resulting figure is similar to the original square but different in size and position.

Topic

Geometry Concepts

Description

This image illustrates a rectangle undergoing a combination of dilation, translation, and rotation. The dilation changes the size of the rectangle, the translation moves it to a new position, and the rotation changes its orientation.

This complex transformation demonstrates how multiple transformations can be combined to create a figure that is similar to the original but different in size, position, and orientation. The resulting figure maintains the proportions of the original rectangle.

Topic

Geometry Concepts

Description

This image shows a rectangle undergoing a combination of dilation and rotation. The dilation changes the size of the rectangle while maintaining its proportions, and the rotation changes its orientation.

This transformation demonstrates how a figure can be both resized and reoriented while maintaining its shape. The resulting figure is similar to the original rectangle but different in size and orientation.

Topic

Geometry Concepts

Description

This image depicts a triangle undergoing a rotation transformation. The rotation changes the orientation of the triangle without altering its size or shape.

This transformation demonstrates how a figure can be moved around a fixed point (the center of rotation) while maintaining its congruence to the original shape. The resulting triangle is identical to the original in all aspects except its orientation.

Topic

Geometry Concepts

Description

This image shows a triangle undergoing a translation transformation. The translation moves the triangle to a new position without changing its size, shape, or orientation.

This transformation demonstrates how a figure can be moved in a straight line without any other changes. The resulting triangle is congruent to the original and maintains all its properties, only differing in its position.

Topic

Geometry Concepts

Description

This image illustrates a triangle undergoing a combination of translation and rotation. The translation moves the triangle to a new position, and the rotation changes its orientation.

This composite transformation demonstrates how multiple transformations can be applied sequentially. The resulting triangle is congruent to the original but different in both position and orientation.

Topic

Geometry Concepts

Description

This image shows a triangle undergoing a combination of dilation and translation performed twice. The dilation changes the size of the triangle while maintaining its shape, and the translations move it to new positions.

This complex transformation demonstrates how multiple transformations can be applied repeatedly. The resulting triangles are similar to the original but differ in size and position.

Topic

Geometry Concepts

Description

This image depicts a trapezoid reflected across a horizontal line. Reflection creates a mirror image of the original figure across a line of reflection.

This transformation demonstrates how a figure can be flipped over a line to create its mirror image. The resulting trapezoid is congruent to the original but inverted vertically.

Teacher's Script: "Observe how the trapezoid is reflected across the horizontal line. What properties of the trapezoid remain unchanged? How does the orientation of the trapezoid change after reflection? Can you identify the line of reflection?"

Topic

Geometry Concepts

Description

This image shows a kite reflected across a horizontal line, followed by a dilation. Reflection creates a mirror image of the original figure across a line of reflection. Dilation changes the size of the original figure but keeps it proportional.

This transformation demonstrates how a figure can be flipped over a line to create its mirror image. The resulting kite is similar to the original but inverted vertically.

Topic

Geometry Concepts

Description

This image illustrates an irregular hexagon reflected across a vertical line. Reflection creates a mirror image of the original figure across a line of reflection.

This transformation demonstrates how a complex figure can be flipped over a vertical line to create its mirror image. The resulting hexagon is congruent to the original but reversed horizontally.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

Use these clip art images and the background grid to test if the right triangles are similar.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF also has sides 5, 4, and 6. The SSS Postulate ensures that these triangles are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF has sides 5, 7, and 6. Because corresponding sides are not all congruent, then the triangles are not congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6, and triangle DEF has sides 5 and 6, but no information on the third side. As a result, there isn't enough information to know if they are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Both triangles have two sides (5 and 6) and an included angle of 60°. As a results of the SAS Postulate, the triangles are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6 with an included angle of 60°, and triangle DEF has sides 5 and 6 with an included angle of 62°. Because corresponding angles are not congruent, then the triangles are not congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are congruent. Both triangles have angles of 63°, 60°, and 57°, but no information on side lengths. As a result, we can't conclude if the triangles are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles on a grid are congruent. Both triangles appear identical in shape and orientation, positioned differently on the grid. Using the grid, you can see that corresponding sides are congruent. Therefore the triangles are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two shapes on a grid are congruent. The shapes appear as two congruent triangles within a diamond shape, with each triangle reflected across the center axis. Using the grid, you can see that corresonding sides are congruent. Therefore, the triangles are congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles on a grid are congruent. The triangles have differing shapes and orientations on the grid, suggesting different side lengths or angles. Therefore, they are not congruent.

Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.

Topic

Geometric Shapes

Description

Determine if two triangles, ABC and DEF, are similar. Triangle ABC has sides 10, 8, and 12, while triangle DEF has sides 5, 4, and 6. Triangles are similar if corresponding sides are proportional. Here, the ratio of corresponding sides is 2:1 (10:5, 8:4, 12:6). Thus, the triangles are similar. Therefore, the answer is Yes, the triangles are similar.