CORRESPONDING SIDES

Corresponding Sides

Definition Of Corresponding Sides

If the relative position of two sides is same in two figures, then they are called Corresponding Sides.

More About Corresponding Sides

Corresponding sides are proportional in similar figures.

Video Examples: Corresponding Angles and Sides

Example of Corresponding Sides

EXAMPLE OF Converging Lines

In the figure, triangles ABC and XYZ are similar.
The relative position of AB and XY is same, so they are corresponding sides.
Similarly, BC and YZ, and AC and XZ, are corresponding sides.

Solved Example on Corresponding Sides

Ques: If the pentagons shown are similar, identify the corresponding sides.

example of Corresponding Sides

Choices:

A. Corresponding_Sides and
B.  and
C.  and
D.  and
Correct Answer: A

Solution:

Step 1: Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.
Step 2: So, PQ/AB = QR/BC = RT/CD = TS/DE = SP/EA [Proportion of sides.]
Step 3: Here, Corresponding_Sides and are corresponding sides.

Quick Summary

Corresponding sides have the same relative position in different figures.
In similar figures, the ratios of corresponding sides are equal (proportional).

\[ null \]

🍎 Teacher Insights

Use visual aids and hands-on activities (e.g., using similar triangles created by shadows) to help students understand the concept of corresponding sides. Emphasize the importance of correct labeling and notation when stating similarity or congruence.

🎓 Prerequisites

Ratios and Proportions
Basic Geometric Shapes (Triangles, Quadrilaterals, Polygons)
Understanding of Angles
Concept of Similarity

Check Your Knowledge

Q1: Triangles ABC and DEF are similar. AB = 4, DE = 8, BC = 6. What is the length of EF?

3 6 12 16

Q2: Quadrilaterals PQRS and WXYZ are similar. Which sides correspond?

PQ and XY QR and WX RS and WZ SP and YZ

Frequently Asked Questions

Q: How do you identify corresponding sides?
A: Look for sides that are in the same relative position in the two figures. Consider the order of vertices in the similarity statement (e.g., if triangle ABC ~ triangle XYZ, then AB corresponds to XY, BC corresponds to YZ, and AC corresponds to XZ).

Q: Are corresponding sides always congruent?
A: No, corresponding sides are congruent in congruent figures. In similar figures, corresponding sides are proportional, meaning they have the same ratio, but not necessarily the same length.