UPSKILL MATH PLUS
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Learn moreIn the given figure, \(UB \parallel AT\) and \(CU \equiv CB\). Prove that \(\triangle CUB \sim \triangle CAT\) and hence \(\triangle CAT\) is isosceles.
Proof:
| Statements | Reasons | |
| 1 | \(\angle CUB = \angle CBU\) | |
| 2 | \(\angle CUB = \angle CAT\) | |
| 3 | \(\angle CBU = \angle CTA\) | |
| 4 | \(\angle UCB = \angle ACT\) | |
| 5 | \(\triangle CUB \sim \triangle CAT\) | |
| 6 | \(CA = CT\) | |
| 7 | \(\triangle CAT\) is an isosceles triangle |
Answer variants:
Since \(\angle CUB = \angle CBU\) and \(\angle CAT = \angle CTA\)
By AAA Similarity criteria(1,2,4)
By AAA Similarity criteria(1,2,3)
By AAA Similarity criteria(2,3,4)
Given that \(UB \parallel AT\), corresponding angles are equal if \(CT\) is transversal.
Given that in \(\triangle CUB\), \(CU = CB\).
Common angle
Opposite sides of equal angle are equal.
Given that \(UB \parallel AT\), corresponding angles are equal if \(CA\) is transversal.
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