Illustrative Math Alignment: Grade 8 Unit 1
Rigid Transformations and Congruence
Lesson 14: Alternate Interior Angles
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Topic |
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Math Example--Geometric Transformation--Transformations: Example 48 | Math Example--Geometric Transformation--Transformations: Example 48
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 49 | Math Example--Geometric Transformation--Transformations: Example 49
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 5 | Math Example--Geometric Transformation--Transformations: Example 5
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 50 | Math Example--Geometric Transformation--Transformations: Example 50
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 51 | Math Example--Geometric Transformation--Transformations: Example 51
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 52 | Math Example--Geometric Transformation--Transformations: Example 52
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 53 | Math Example--Geometric Transformation--Transformations: Example 53
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 54 | Math Example--Geometric Transformation--Transformations: Example 54
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 55 | Math Example--Geometric Transformation--Transformations: Example 55
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 56 | Math Example--Geometric Transformation--Transformations: Example 56
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 6 | Math Example--Geometric Transformation--Transformations: Example 6
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 7 | Math Example--Geometric Transformation--Transformations: Example 7
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 8 | Math Example--Geometric Transformation--Transformations: Example 8
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 9 | Math Example--Geometric Transformation--Transformations: Example 9
This is part of a collection of math examples that focus on geometric transformations. |
Definition of Transformations |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 1 | Equations Using the Exterior Angle Theorem--Example 1TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 10 | Equations Using the Exterior Angle Theorem--Example 10TopicEquations DescriptionThis example illustrates a more complex application of the Exterior Angle Theorem in solving triangle-related equations. In this scenario, we have a triangle with one known interior angle of 35°, an unknown interior angle y, and an unknown exterior angle x. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the equation is set up as x = 35° + y. Furthermore, the angles 3x and x are supplementary, allowing you to solve for x. Having solved for x, you can then solve for y. |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 2 | Equations Using the Exterior Angle Theorem--Example 2TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 3 | Equations Using the Exterior Angle Theorem--Example 3TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 4 | Equations Using the Exterior Angle Theorem--Example 4TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 5 | Equations Using the Exterior Angle Theorem--Example 5TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 6 | Equations Using the Exterior Angle Theorem--Example 6TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 7 | Equations Using the Exterior Angle Theorem--Example 7TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 8 | Equations Using the Exterior Angle Theorem--Example 8TopicEquations |
Applications of Triangles |
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Math Example--Solving Equations--Equations Using the Exterior Angle Theorem--Example 9 | Equations Using the Exterior Angle Theorem--Example 9TopicEquations DescriptionThis example presents a more challenging application of the Exterior Angle Theorem in solving triangle-related equations. In this scenario, we have a triangle with one known interior angle of 25°, an unknown interior angle y, and an unknown exterior angle x. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the equation is set up as x = 25° + y. You can also use the fact that x and 2x are supplementary, allowing you to solve for x. By solving for x, you can then solve for y using the triangle equation. |
Applications of Triangles |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 7 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 7TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 8 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 8TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 9 | Equations with Angles from Parallel Lines Cut by a Transversal--Example 9TopicEquations |
Parallel Lines, Applications of Angles and Planes and Applications of Equations and Inequalities |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 1 | Solving Equations with Angle Measures 2--Example 1TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 10 | Solving Equations with Angle Measures 2--Example 10TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 2 | Solving Equations with Angle Measures 2--Example 2TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3 | Solving Equations with Angle Measures 2--Example 3TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 4 | Solving Equations with Angle Measures 2--Example 4TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 5 | Solving Equations with Angle Measures 2--Example 5TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 6 | Solving Equations with Angle Measures 2--Example 6TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 7 | Solving Equations with Angle Measures 2--Example 7TopicEquations DescriptionThis example demonstrates solving equations involving angle measures in a kite. A kite has two pairs of adjacent congruent angles. In this case, we have angles represented as (x+50)°, (x+50)°, (y+20)°, and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the sum of the angles of a triangle is 180°. You can use the triangle equation to solve for y. Once you determine the value for y, you can use that to find x using either the triangle or the quadrilateral equation. In the solution shown, the triangle equation is used. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 8 | Solving Equations with Angle Measures 2--Example 8TopicEquations DescriptionThis example illustrates solving equations involving angle measures in a kite. The kite has two known angles of 70° and 40°, and two unknown angles represented as (x+y)°. To solve this problem, we look at the triangles formed by one of the diagonals of the kite and use the triangle equation. First solve for x with the top triangle. Once you find x, use that value to solve for y in the bottom triangle. You could also use the quadrilateral equation to solve for y. |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 9 | Solving Equations with Angle Measures 2--Example 9TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 | Solving Equations with Angle Measures--Example 1TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 | Solving Equations with Angle Measures--Example 10TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 | Solving Equations with Angle Measures--Example 11TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 | Solving Equations with Angle Measures--Example 12TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 | Solving Equations with Angle Measures--Example 13TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
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Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 | Solving Equations with Angle Measures--Example 14TopicEquations |
Solving Multistep Equations and Applications of Angles and Planes |
