Illustrative Math Alignment: Grade 7 Unit 7

Topic

Geometry

Description

This example combines the concepts of isosceles right triangles and algebraic expressions. The triangle has two equal legs labeled as x, with angles of 45 degrees. Students are challenged to express the area formula using this variable, applying their knowledge of both triangle properties and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the area of a 30-60-90 right triangle. The triangle has a base of 16 units and a height of 8√3 units. Students are guided through applying the area formula to this specific case, which involves working with irrational numbers.

Topic

Geometry

Description

This example combines the properties of 30-60-90 right triangles with algebraic expressions. The triangle has a base of x + 5 and a height of (x + 5)/2 * √3. Students are challenged to express the area formula using these algebraic terms, applying their knowledge of both special right triangles and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the area of a 3-4-5 right triangle. This triangle is a special case of right triangles with integer side lengths. Students are guided through applying the area formula to this specific case, which is straightforward due to its simple dimensions.

Topic

Geometry

Description

This example combines the concept of a 3-4-5 right triangle with algebraic expressions. The triangle's sides are labeled as 3(x + 4), 4(x + 4), and 5(x + 4). Students are challenged to express the area formula using these algebraic terms, applying their knowledge of both special right triangles and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the area of a right triangle with sides 5, 12, and 13 units. Students are guided through applying the area formula to this specific case, which involves a right triangle with integer side lengths that satisfy the Pythagorean theorem.

Topic

Geometry

Description

This example illustrates the calculation of a scalene triangle's area using algebraic expressions. The triangle has sides labeled x, y, z, with a height labeled w from the base x. To find the area, we use the formula A = 1/2 * b * h. In this case, A = 1/2 * x * w = xw / 2.

Topic

Geometry

Description

This example combines the concept of a 5-12-13 right triangle with algebraic expressions. The triangle's sides are labeled as 5(x - 7), 12(x - 7), and 13(x - 7). Students are challenged to express the area formula using these algebraic terms, applying their knowledge of both special right triangles and algebraic manipulation.

Topic

Geometry

Description

This example introduces the concept of perimeter calculation for a scalene triangle. The triangle has sides measuring 5, 7, and 9 units. Students are guided through the process of calculating the perimeter by simply adding the lengths of all sides.

Topic

Geometry

Description

This example introduces the concept of perimeter calculation for a scalene triangle using algebraic expressions. The triangle has sides labeled x, y, and z. Students are guided through the process of expressing the perimeter using these variables.

Topic

Geometry

Description

This example focuses on calculating the perimeter of an acute triangle with specific side lengths. The triangle has sides measuring 10, 11, and 12 units, with angles of 50 and 60 degrees. Students are guided through the process of adding these side lengths to find the perimeter.

Topic

Geometry

Description

This example combines the concept of perimeter calculation for an acute triangle with algebraic expressions. The triangle has sides labeled as x - 3, x - 4, and x. Students are challenged to express the perimeter formula using these algebraic terms, applying their knowledge of both geometry and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the perimeter of an obtuse triangle with specific side lengths. The triangle has sides measuring 15, 6, and 18 units, with an obtuse angle of 120 degrees. Students are guided through the process of adding these side lengths to find the perimeter.

Topic

Geometry

Description

This example combines the concept of perimeter calculation for an obtuse triangle with algebraic expressions. The triangle has sides labeled as x + 1, x + 2, and x + 4, with an obtuse angle of 120 degrees. Students are challenged to express the perimeter formula using these algebraic terms, applying their knowledge of both geometry and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the perimeter of an isosceles triangle with specific side lengths. The triangle has two equal sides measuring 10 units and a base of 8 units. Students are guided through the process of adding these side lengths to find the perimeter.

Topic

Geometry

Description

This example combines the concept of perimeter calculation for an isosceles triangle with algebraic expressions. The triangle has two equal sides labeled as x + 4 and a base of x - 3. Students are challenged to express the perimeter formula using these algebraic terms, applying their knowledge of both geometry and algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the perimeter of an equilateral triangle with specific side lengths. The triangle has all sides measuring 15 units. Students are guided through the process of adding these side lengths to find the perimeter, emphasizing the simplicity of calculations for equilateral triangles.

Topic

Geometry

Description

This example demonstrates how to calculate the area of an acute triangle. The triangle has angles labeled as 50° and 60°, with a base measuring 12 units and a height of 8 units. To find the area, we use the formula A = 1/2 * b * h. In this case, A = 1/2 * 12 * 8 = 48 square units.

Understanding the area of triangles is a fundamental concept in geometry that applies to various real-world situations. This collection of examples helps students visualize different types of triangles and compute their areas accurately using given dimensions.

Topic

Geometry

Description

This example combines the concept of perimeter calculation for an equilateral triangle with algebraic expressions. The triangle has all sides labeled as 2x + 3. Students are challenged to express the perimeter formula using this algebraic term, applying their knowledge of both geometry and algebraic manipulation.

Topic

Geometry

Description

This example demonstrates the process of finding the perimeter of a right triangle when only two sides are given. The triangle has sides measuring 7 and 12 units. Students are guided through using the Pythagorean Theorem to find the length of the hypotenuse before calculating the perimeter.

Topic

Geometry

Description

This example demonstrates the process of finding the perimeter of a right triangle with algebraic expressions for its sides. The triangle has legs labeled as x - 2 and 2x. Students are guided through using the Pythagorean Theorem to find the hypotenuse and then calculating the perimeter using algebraic manipulation.

Topic

Geometry

Description

This example focuses on calculating the perimeter of an isosceles right triangle. The triangle has two equal sides of length 12 units and angles of 45 degrees. Students are guided through the process of using the Pythagorean Theorem to find the hypotenuse and then calculating the perimeter.

Topic

Geometry

Description

This example combines the concept of isosceles right triangles with algebraic expressions. The triangle has two equal sides labeled as x + 2 and angles of 45 degrees. Students are challenged to use the Pythagorean Theorem to find the hypotenuse and then express the perimeter using algebraic terms.

Topic

Geometry

Description

This example focuses on calculating the perimeter of a 30-60-90 right triangle. The triangle has sides of 12 and 24 units, with angles of 30 and 60 degrees. Students are guided through the process of using the Pythagorean Theorem to find the third side and then calculating the perimeter.

Topic

Geometry

Description

This example combines the concept of 30-60-90 right triangles with algebraic expressions. The triangle has sides labeled as x - 10 and 2(x - 10), with angles of 30 and 60 degrees. Students are challenged to use the Pythagorean Theorem to find the third side and then express the perimeter using algebraic terms.

Topic

Geometry

Description

This example demonstrates the process of finding the perimeter of a right triangle with sides of 6 and 8 units. Students are guided through using the Pythagorean Theorem to find the hypotenuse and then calculating the perimeter by adding all three sides.

Topic

Geometry

Description

This example combines the concept of right triangle perimeter with algebraic expressions. The triangle has sides labeled as 3(x + 4) and 4(x + 4). Students are challenged to use the Pythagorean Theorem to find the hypotenuse and then express the perimeter using algebraic terms.

Topic

Geometry

Description

This example demonstrates the process of finding the perimeter of a right triangle with sides of 5 and 12 units. Students are guided through using the Pythagorean Theorem to find the hypotenuse and then calculating the perimeter by adding all three sides.

Topic

Geometry

Description

This example introduces students to calculating the area of an acute triangle using algebraic expressions. The triangle has angles of 50 and 60 degrees, with the base labeled as x and the height as x - 4. Students are tasked with expressing the area formula using these variables.

Topic

Geometry

Description

This example combines the concept of right triangle perimeter with complex algebraic expressions. The triangle has sides labeled as 5(x + 10) and 12(x + 10). Students are challenged to use the Pythagorean Theorem to find the hypotenuse and then express the perimeter using algebraic terms.

Topic

Geometry

Description

This example demonstrates the calculation of area for an obtuse triangle. The triangle has a base of 15 units, a height of 8 units, and includes a 120-degree angle. Students are guided through the process of applying the area formula for this specific case.

Topic

Geometry

Description

This example combines the concepts of obtuse triangles and algebraic expressions. The triangle has a base of x + 1 and a height of x - 1, with a 120-degree angle. Students are challenged to express the area formula using these algebraic terms.

Topic

Geometry

Description

This example focuses on calculating the area of an isosceles triangle. The triangle has two equal angles of 65° and a base angle of 50°. The base is 8 units long, and the height is 10 units. Students are guided through applying the standard area formula to this specific case.

Topic

Geometry

Description

This example combines isosceles triangles with algebraic expressions. The triangle has two equal angles of 65° and a base angle of 50°. The base is expressed as x - 3, and the height as x + 3. Students are challenged to formulate the area using these algebraic terms.

Topic

Geometry

Description

This example focuses on calculating the area of an equilateral triangle. The triangle has all angles equal to 60°, a base of 12 units, and a height of 6√3 units. Students are guided through applying the area formula using these specific dimensions, which involve a square root.

Topic

Geometry

Description

This image shows two triangles labeled ABC and DEF. The triangles are oriented differently but have corresponding sides and angles marked as congruent. The table below the triangles lists the congruent sides and angles.

In this topic, students explore 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.

Topic

Geometry

Description

This image shows two triangles labeled ABC and DEF. The triangles are oriented differently, but the corresponding sides are marked as congruent. The given information lists AB ≅ FE, AC ≅ DF, and BC ≅ DE.

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.

Topic

Geometry

Description

This image shows two triangles labeled ABC and DEF. The triangles have corresponding angles marked as congruent (∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F). However, no information is given about the side lengths.

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.

Topic

Geometry

Description

This image shows two triangles ABD and CBD sharing a common side BD. Given information includes AD ≅ CD and AB ≅ BC. The solution points out that BD is common to both triangles and uses this to conclude that the triangles are congruent by the SSS Postulate.

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.

Topic

Geometry

Description

The image shows two triangles, each intersecting a circle at two points and one of whose angles is a central angle. The triangles are ABC and DCE. 

We are given that AB ≅ DE. Furthermore, each triangle has two sides that correspond to radii of the circle and therefore those sides are congruent. As a result of the SSS Postulate, since corresponding sides of the triangle are congruent, then the triangles are congruent.

Topic

Geometry

Description

The 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.

Topic

Geometry

Description

The 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.

Topic

Geometry

Description

The 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.

Topic

Transformations

Description

A 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."

Topic

Transformations

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."

Topic

Transformations

Description

Triangle 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.

Topic

Transformations

Description

Triangle 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.

Topic

Transformations

Description

Triangle 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.

Topic

Transformations

Description

Triangle 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.

Topic

Transformations

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.