Exercise 3

Chapter 4, Section 4-1, Page 151
enVision Geometry 1st Edition by Al Cuoco
ISBN: 9780328931583

Solution

Verified

We must observe if the corresponding side lengths or angles are equal.

(a)\textbf{(a)}

No. Comparing the sides lengths, AB=JKAB=JK, BC=KLBC=KL, and CD=LMCD=LM. However, DEMNDE\ne MN and EANJEA\ne NJ so ABCDE≇JKLMNABCDE\not\cong JKLMN.

(b)\textbf{(b)}

Yes. All corresponding sides have the same measure: AB=VWAB=VW, CD=WXCD=WX, DE=XYDE=XY, EF=YZEF=YZ, and EA=ZVEA=ZV

A possible composition of rigid motions is to first reflect ABCDEABCDE about the xx-axis then translate 10 units to the left:

(T10,0Rx-axis)(ABCDE)=VWXYZ\color{#c34632}{(T_{\langle -10,0\rangle} \circ R_{x\text{-axis}})(ABCDE)=VWXYZ}

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