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Chapter 5: Q42 (page 189)

Given: Rectangle RSTW; equilateral 螖YWT and STW.

State what is true of 螖RYZ.

Write a paragraph proof.

Short Answer

Expert verified

螖RYZis an equilateral triangle.

Step by step solution

01

Step 1. Consider the diagram.

Here, RSTW is a rectangle and 螖WYT and 螖STZ are equilateral triangle.

02

Step 2. State the proof.

As RSTW is a rectangle and 螖WYTand 螖STZare equilateral triangle.

WT=RS=WY=YTST=RW=SZ=ZT

In 螖WYRand 螖RSZ,

WR=SZ (Given)

鈭�YWR=鈭�RSZ (As 鈭�YWT+鈭�TWR=鈭�RST+鈭�TSZ).

WY=RS (Given)

By SAS rule,

螖WYR鈮�螖RSZ

By congruent property,

RY=RZ 鈥︹�� (1)

In 螖RSZand 螖YTZ,

SR=YT (Given)

鈭�RSZ=鈭�YTZ

SZ=ZT (Given)

By SAS rule,

螖RSZ鈮�螖YTZ

By congruent property,

RZ=YZ

Since, RZ=RY

Therefore, RY=RZ=YZ.

So, 螖RYZis an equilateral triangle.

03

Step 3. State the conclusion.

Therefore, 螖RYZis an equilateral triangle (proved).

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