Question

8. In AABC, AB = AC. BD and CE are perpendiculars drawn to AC and AB respectively. Prove that
BD =CE.

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Answer 1

in triangle ABC

AB=AC given

angle ABC=angle ACB or

angle EBC=angle DCB

in triangle BEC and DCB

angle EBC =angle DCB

BC=BC common

angle BDC= angle CEB each equal to 90°

therefore

triangle EBC congruent to triangle DCB

by SAS