Use the following Media4Math resources with this Illustrative Math lesson.
Thumbnail Image | Title | Body | Curriculum Nodes |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 16 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 16
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 17 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 17
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 18 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 18
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 19 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 19
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 2 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 2
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 20 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 20
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 21 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 21
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 22 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 22
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 23 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 23
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 1 | Solving Equations Using Angle Properties: Example 1TopicEquations DescriptionThis example demonstrates solving equations using angle properties, specifically focusing on supplementary angles. Supplementary angles are two angles that add up to 180 degrees. In this case, we have one known angle of 135° and an unknown angle x. To solve such equations, we use the fundamental property of supplementary angles: their sum equals 180°. |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 10 | Solving Equations Using Angle Properties: Example 10TopicEquations DescriptionThis example illustrates solving equations using angle properties, focusing on parallel lines cut by a transversal and supplementary angles. When parallel lines are cut by a transversal, pairs of supplementary angles are formed, meaning they sum to 180°. In this scenario, we have one known angle of 118° and an unknown angle x. However, angle y and the 118° angle are alternate exterior angles, which are congruent. This means we can set up this equation using the property of supplementary angles: 118 + x = 180 |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 2 | Solving Equations Using Angle Properties: Example 2TopicEquations DescriptionThis example illustrates solving equations using angle properties, focusing on supplementary angles. Supplementary angles are two angles that sum to 180 degrees. In this scenario, we have one known angle of 75° and an unknown angle x. The equation for supplementary angles is always in the form: angle1 + angle2 = 180°. Here, we can write 75 + x = 180. To solve for x, we subtract 75 from both sides: x = 180 - 75, giving us x = 105°. |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 3 | Solving Equations Using Angle Properties: Example 3TopicEquations DescriptionThis example demonstrates solving equations using angle properties, specifically focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (36° and 72°) and an unknown angle x. This unknown angle x is vertical (and therefore congruent) to angle z. The angles 36, 72, and z form a straight, but since z is congruent to x, we can write the sum of this straight angle: x + 36 + 72 = 180 x = 72° |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 4 | Solving Equations Using Angle Properties: Example 4TopicEquations DescriptionThis example illustrates solving equations using angle properties, focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (42° and 55°) and an unknown angle x. However, angle x is vertical (and therefore congruent) to angle y. The equation can be set up based on the fact that the sum of angles on a straight line is 180°. Thus, we have: 42 + 55 + x = 180 |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 5 | Solving Equations Using Angle Properties: Example 5TopicEquations DescriptionThis example demonstrates solving equations using angle properties, specifically focusing on complementary angles and the exterior angle theorem. Complementary angles are two angles that sum to 90°, while the exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this scenario, we have a right angle (90°), an exterior angle (125°), and an unknown angle x. Using the exterior angle theorem, we can set up the equation: x + 90 = 125. To solve for x, we subtract 90 from both sides: x = 35°. |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 6 | Solving Equations Using Angle Properties: Example 6TopicEquations DescriptionThis example illustrates solving equations using angle properties, focusing on an isosceles right triangle. An isosceles right triangle has a right angle (90°) and two equal angles. In this scenario, we have the right angle given, and the two unknown equal angles represented by x. The equation can be set up based on the fact that the sum of angles in a triangle is 180°. Thus, we have: 90 + x + x = 180, or simplified, 90 + 2x = 180 To solve for x, we first subtract 90 from both sides: 2x = 90. Then, dividing both sides by 2, we get: x = 45°. |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 7 | Solving Equations Using Angle Properties: Example 7TopicEquations DescriptionThis example demonstrates solving equations using angle properties, specifically focusing on parallel lines cut by a transversal and same side interior angles. When parallel lines are cut by a transversal, same side interior angles are supplementary, meaning they sum to 180°. In this scenario, we have one known angle of 112° and an unknown angle x. The 112° angle is vertical to the same side interior angle paired with x. The equation can be set up as: 112 + x = 180 |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 8 | Solving Equations Using Angle Properties: Example 8TopicEquations DescriptionThis example illustrates solving equations using angle properties, focusing on parallel lines cut by a transversal and alternate interior angles. When parallel lines are cut by a transversal, alternate interior angles are congruent, meaning they have the same measure. In this scenario, we have one known angle of 48° and an unknown angle x. Since x and y are alternate interior angles, they are congruent. We can now use the property of supplementary angles to solve for x: x + 48 = 180 x = 132° |
Applications of Equations and Inequalities and Definition of an Angle | |
Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 9 | Solving Equations Using Angle Properties: Example 9TopicEquations DescriptionThis example demonstrates solving equations using angle properties, specifically focusing on parallel lines cut by a transversal and alternate interior angles. When parallel lines are cut by a transversal, alternate interior angles are congruent, meaning they have the same measure. In this scenario, we have one known angle of 43° and an unknown angle x. However, angle x and angle y are alternate interior angles and are congruent. This means that x and teh 43° angle are same side interior angles, which are supplementary. We set up this equation: |
Definition of an Angle and Applications of Equations and Inequalities | |
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 1 | Solving Equations Using Triangle Properties: Example 1TopicEquations DescriptionThis example focuses on solving equations using the properties of similar isosceles triangles. Isosceles triangles are characterized by having two equal sides and two equal base angles. In this case, we have two similar isosceles triangles, which means they share the same shape but may differ in size. The equation to be solved involves finding the unknown angle x, given that one of the angles is 20°. The property of vertical angles tells us that the angle vertical to the 20° angle is also 20° |
Applications of Equations and Inequalities and Applications of Triangles | |
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 10 | Solving Equations Using Triangle Properties: Example 10TopicEquations DescriptionThis example, similar to Example 9, involves solving equations using the properties of a kite and applying the exterior angle theorem. We are again given one angle of 40° and two unknown angles, y and x. The goal is to set up and solve equations to find the values of y and x using the properties of kites and the exterior angle theorem. Key properties to consider: |
Applications of Equations and Inequalities and Applications of Triangles | |
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 2 | Solving Equations Using Triangle Properties: Example 2TopicEquations DescriptionThis example explores solving equations using the properties of similar isosceles triangles, building upon the concepts introduced in Example 1. In this case, we have two similar isosceles triangles with one known angle of 70° and an unknown angle x. The goal is to determine the value of x using triangle properties and algebraic techniques. |
Applications of Equations and Inequalities and Applications of Triangles | |
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 3 | Solving Equations Using Triangle Properties: Example 3TopicEquations DescriptionThis example focuses on solving equations involving parallel lines cut by a transversal, a fundamental concept in geometry. The problem presents two parallel lines intersected by two transversals that also form a triangle. We are given that one angle measures 120° and the corresponding angle can be expressed as (y + 40)°. The goal is to determine the value of y using the properties of angles formed by parallel lines and a transversal. When parallel lines are cut by a transversal, several important angle relationships are formed: |
Applications of Equations and Inequalities and Applications of Triangles | |
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 4 | Solving Equations Using Triangle Properties: Example 4TopicEquations DescriptionThis example demonstrates solving equations using the Exterior Angle Theorem in the context of parallel lines cut by a transversal, two crucial concepts in geometry. The problem presents a triangle with two known interior angles of 80° and y, and an unknown exterior angle x°. We are also given that 80 - y = 50, which simplifies to y = 30. The goal is to determine the value of x using the properties of triangles and the Exterior Angle Theorem. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Wo we get x = 80 + 30, or x = 110. |
Applications of Equations and Inequalities and Applications of Triangles |