Q-12. Prove that angles opposite to …
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Posted by Arun Kushwah 3 years, 9 months ago
- 1 answers
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Yogita Ingle 3 years, 9 months ago
Given: In the isosceles ∆XYZ, XY = XZ.
To prove ∠XYZ = ∠XZY.
Construction: Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.
Proof:
Statement
1. In ∆XYM and ∆XZM,
(i) XY = XZ
(ii) XM = XM
(iii) ∠YXM = ∠ZXM
2. ∆XYM ≅ ∆XZM
3. ∠XYZ = ∠XZY. (Proved)
Reason
1.
(i) Given.
(ii) Common side.
(iii) XM bisects ∠YXZ.
2. By SAS criterion.
3. CPCTC.
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