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