Question

In $△PQR$ above, $PR=QR$. Which of the following must be true?

• A. $u=x$
• B. $x=v$
• C. $x=z$
• D. $y=x$
• E. $y=z$

Answer 1

The correct option is E $y=z$

Given, in $△$$PQR$, $PR$ $=$ $QR$

We know that, if two sides of a triangle are equal, the angles opposite to those two equal sides are also equal.

Hence, $\angle RPQ$ $=$ $\angle PQR$

$⟹u°$ $=$ $v°$

We know that, sum of angles on a straight line is equal to $180$.

Thus, $y°$ $+$ $v°$ $=$ $180°$ and $u°$ $+$ $z°$ $=$ $180°$

$y°$ $=$ $180°$ $-$ $u°$ and $z°$ $=$ $180°$ $-$ $v°$

As, $u°$ $=$ $v°$, let $u°$ $=$ $v°$ $=$ $t°$

$y°$ $=$ $180°$ $-$ $t°$ and $z°$ $=$ $180°$ $-$ $t°$

$y°$ $=$ $z°$.