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Why is this concept useful?: Understanding corresponding sides helps us understand if two shapes are congruent. The corresponding sides of congruent shapes are equal in length. This concept is also used to understand similar shapes. The corresponding sides of similar shapes are proportional.
Where does this concept fit into the curriculum?: Grade 8, High School Geometry

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What are corresponding sides?

Corresponding sides or angles are a pair of matching sides or angles that are in the same spot in two different shapes.

How to use corresponding sides in problems:

In the SSS – Congruence rule says that in two triangles, if all the three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles can be said to be congruent.

Two triangles are said to be similar if all corresponding sides are in the same ratio and corresponding angles are the same.

Sample Math Problems

1. Assume the following triangles are similar. What would be the length of a?

Answer:
In this, we know that AB and ED are corresponding sides. As the triangles are similar, their sides will have the same ratios.

First find the ratios of AB/DE = 10/16 = 5/8

So the ratio of BC/EF will also be 5/8.

9/EF = 5/8

EF = 9*8/5 = 72/5 = 14.4

2. Two triangles are said to be similar if their sides are:

a) Proportional
b) Equal
c) Parallel
d) Perpendicular

Answer:
Answer: A – proportional

3. Identify the point in Figure 2 that corresponds to point M

Answer: D

4. Identify the side in figure 2 that corresponds to the line segment BC in figure 1

Answer: IJ

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Practice Math Problems

For questions 1-2 use the following diagram:

1. What is the corresponding point in figure 1 to point H?

2. What is the corresponding line segment in Figure 2 to AD?

3. If side A in triangle ABC corresponds to side D in triangle DEF and has a ratio 1:2. Then what is the length of side E if side B is 4.

4. If side A in triangle ABC corresponds to side D in triangle DEF and has a ratio 1:2. Then what is the length of side E if side B is 4.

Geometry Worksheets

Corresponding Sides

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