in a tri anc the altitude BD and ce with respect to the side ac and ab RESPECTIVELY are equal prove that ab = ac
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Answer:
Here we use ASA congruenceASA(angle side angle):Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the other triangle.
Given:
ΔABC is an isosceles∆ with AB = AC, BD and CE are altitudes.
To prove:
BD = CE
Proof:
In ΔAEC and ΔADB
∠A = ∠A. (Common)
∠AEC = ∠ADB (each 90°)
AB = AC (Given)
Therefore, ΔAEC ≅ ΔADB[by AAS congruence rule]
Thus, BD = CE (by CPCT)
Hence , altitudes BD & CE are equal.
Step-by-step explanation:
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