Question

Complete the congruence statement along with the criterion used :​

Answer 1

Answer :-

• △BCA ≅ △BTA

• △QRS ≅ △QTR

Given :-

• Figure 1 - BC = BT , BA ⊥ TC , AC = AT , AB bisect ∠B
• Figure 2 - PT = QR , QP = QT , QS = RS , ∠SQR = ∠PTQ , ∠TPQ = ∠SRQ

To Find :-

• △BCA ≅ ?

• △QRS ≅ ?

Explanation :-

➤ In Figure 1 ( ΔBCA and ΔBTA )

$\rm \implies BC = BT \qquad \bold {[Given]}$

$\rm \implies AC = AT \qquad \bold {[Given]}$

$\rm \implies BA = AB \qquad \bold {[Common]}$

$\underline { \boxed { \rm \bold { Hence,\triangle BCA \cong \triangle BTA }}}$

➤ In Figure 2 ( ΔQRS and ΔQTR )

$\rm \implies PT = QR \qquad \qquad \; \; \bold {[Given]}$

$\rm \implies \angle SQR = \angle PTQ \qquad \bold {[Given]}$

$\rm \implies \angle TPQ = \angle SRQ \qquad \bold {[Given]}$

$\underline { \boxed { \rm \bold { Hence,\triangle QRS \cong \triangle QTR }}}$

Hence, △BCA ≅ △BTA and △QRS ≅ △QTR.

@Agamsain