Question

In ΔRST, RS = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?​

Answer 1

Answer:

Angle -side -Angle criteria can be used to construct triangle RST

Answer 2

$\orange{\bold{\underbrace{\overbrace{IN \:∆RTS , we \:GOT, }}}}$

$\huge{ \color{purple}{ \colorbox{grey}{☞∠SRT = 45° }}}$

$\huge{ \color{purple}{ \colorbox{grey}{☞∠RST = 45° }}}$

USING THE Angle sum Property of a ∆,

☞∠SRT + ∠RST + ∠RTS = 180°

☞45° + 45° + ∠RTS = 180°

☞90° + ∠RTS = 180°

☞∠RTS = 180° - 90°

☞∠RTS = 90° .

$\sf \pink{ \underline{SO\: ΔRST\: is\: a \:right-angled \:Δ}}$

${ \boxed{\fcolorbox{black}{pink}{Hypotenuse ☞RS = 5}}}$

We have, two ∠ equal to 45° and hypotenuse as 5cm.

Angle - Side - Angle(A-S-A) ,,,criterion can be used to construct ∆RST .