congruent because the images, the pre-image, and the image, - PowerPoint PPT Presentation

D AY 51 – I DENTIFYING C ONGRUENT SIDES OF A TRIANGLE

I NTRODUCTION When a figure undergoes a rigid motion, its shape and size do not change. As a result, it becomes easy to trace the sides that originate from the initial sides before the transformation. These sides, actually must be congruent. In this lesson, we are going to learn how to identify congruent sides of identical figures.

V OCABULARY  Congruent sides They are sides that are equal

In translation When an image is translated, the orientation does not change. Hence corresponding sides are congruent because the images, the pre-image, and the image, congruent one having undergone a rigid motion. The corresponding sides are those that occupy similar positions and have the same orientation. H Y S G R T

The congruent sides are SH and RY, HG and YT, and SG and RT In reflection, rotation and glide reflection The best trick of identifying congruent sides is comparing the sides are finding out which ones have approximately same sizes. Another trick is trying to figure out how can we take a figure, take it through a number of rigid motions till we exactly fit it on the original figure. By that, we would be able to trace how the orientation of the original side changed to get the final side. Thus, a pair of congruent figures sides is achieved. We use the same procedure to identify others too.

Example 1 List the pairs of correct sides among the following B (i) K C G H Y A Q (ii). N B G M

Solution (i). In the figure above, ABC appears to have been rotated then translated to get GHK. Thus, rigid motion exists and corresponding sides are congruent. Comparing the lines, we get that 𝐷𝐶 = 𝐻𝐼, 𝐷𝐵 = 𝐼𝐿 and 𝐷𝐶 = 𝐻𝐿. (ii). In the figure below, BGN appears to have been reflected then rotated to get MNQ. Thus, rigid motion exists and corresponding sides are congruent. Comparing the lines, we get that NB = 𝑍𝑅, 𝐶𝐻 = 𝑅𝑁 and 𝑂𝐻 = 𝑁𝑍.

HOMEWORK  Find the congruent sides of the following figures T F H E S G

A NSWERS TO HOMEWORK 𝐹𝐺 = 𝐼𝑈, 𝐺𝐻 = 𝑈𝑇, 𝐻𝐹 = 𝑇𝐼

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