Question

In the given figure, BX and CY are perpendicular to a line through the vertex A of triangle ABC and Z is the mid-point of BC. Prove that XZ=YZ.
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Answer 1

Step-by-step explanation:

In triangle XBZ AND CYZ ,

BZ = CZ -------- z is the midpoint

angleXBZ=angleYCZ. ------- both angles are 90°

BX =CY --------- Height of ∆ABC

so, by SAS congruency test ,

∆XBZ=∆YCZ

Therefore, by CPCT, XZ=YZ

Answer 2

Step-by-step explanation:

triangles XBZ and YCZ are congruent by SAS

BX=YC

angle XBZ= angleYCZ

BZ=ZC

so by cpct

XZ=ZY