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Common Core (Geometry)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Common Core: HSG-SRT.B.5

The following diagrams show the properties of similar triangles. Scroll down the page for more examples and solutions on how to identify similar triangles and how to use similar triangles to solve problems.

**Finding missing measures using similar triangles**

Use similar triangles to find unknown measures (angles and sides).**Indirect Measurement Using Similar Triangles**

This video explains how to use the properties of similar triangles to determine the height of a tree.

**Use Similar Triangles to Solve Problems**

This lesson works though three examples of solving problems using similar triangles.

Example 1: Fred needs to know how wide a river is. He takes measurements as shown in the diagram. Determine the river's width

Example 2: Determine the ratio of the areas of the two similar triangles.

Example 3: If the area of the smaller triangle is 20 m^{2},
determine the area of the bigger triangle.
**Application of Similar Triangles**

Example:

An abstract artist wants to create two proportional triangular paintings. The dimensions are as shown. How long should the two missing sides be in the second painting?**How Tall Is It (The height of the light pole)**

A lesson on using similar triangles and proportions to solve for a missing length.**Using Similar Triangles**

Examples of applications with similar triangles.

1. A tree with a height of 4 m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 20 m long?

2. Jordan wants to measure the width of a river that he can't cross. Help him to figure out the width of the river.**Indirect Measurement using Similar Triangles**

Example:

Benjamin places a mirror 40 ft from the base of an oak tree. When he stands at a distance of 5 ft from the mirror, he can see the top of the tree in the reflection. If Benjamin is 5 ft 8 in tall, what is the height of the oak tree?**Word Problems with Similar Triangles and Proportions**

Examples:

1. Two ladders are leaning against a wall at the same angle. How long is the shorter angle?

2. Campsites R and S are on opposite sides of a lake. What is the distance between the two campsites?

Common Core (Geometry)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Common Core: HSG-SRT.B.5

The following diagrams show the properties of similar triangles. Scroll down the page for more examples and solutions on how to identify similar triangles and how to use similar triangles to solve problems.

Use similar triangles to find unknown measures (angles and sides).

This video explains how to use the properties of similar triangles to determine the height of a tree.

This lesson works though three examples of solving problems using similar triangles.

Example 1: Fred needs to know how wide a river is. He takes measurements as shown in the diagram. Determine the river's width

Example 2: Determine the ratio of the areas of the two similar triangles.

Example 3: If the area of the smaller triangle is 20 m

Example:

An abstract artist wants to create two proportional triangular paintings. The dimensions are as shown. How long should the two missing sides be in the second painting?

A lesson on using similar triangles and proportions to solve for a missing length.

Examples of applications with similar triangles.

1. A tree with a height of 4 m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 20 m long?

2. Jordan wants to measure the width of a river that he can't cross. Help him to figure out the width of the river.

Example:

Benjamin places a mirror 40 ft from the base of an oak tree. When he stands at a distance of 5 ft from the mirror, he can see the top of the tree in the reflection. If Benjamin is 5 ft 8 in tall, what is the height of the oak tree?

Examples:

1. Two ladders are leaning against a wall at the same angle. How long is the shorter angle?

2. Campsites R and S are on opposite sides of a lake. What is the distance between the two campsites?

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