Question

In the given figure, UB || AT and CU ≡ CB Prove that ΔCUB ~ ΔCAT and hence ΔCAT is isosceles.

Answer 1

Statements	Reasons
1. ∠CUB = ∠CBU	∵ In ΔCUB, CU = CB
2. ∠CUB = ∠CAB	∵ UB || AT, Corresponding angle if CA is the transversal.
3. ∠CBU = ∠CTA	CT is transversal UB || AT, Corresponding angle commom angle.
4. ∠UCB = ∠ACT	Common angle
5. ΔCUB ~ ΔCAT	By AAA criteria
6. CA = CT	∵ ∠CAT = ∠CTA
7. Also ΔCAT is isoceles	By 1, 2 and 3 and sides opposite to equal angles are equal.