Question

yx is perpendicular to wz at X between W and Z. wxy=zyx and yw=yz Which congruency statements (HL, AAS, ASA, SAS, and SSS) can you use to conclude that wxy=xy.

Answer 1

Answer:

It is given that , In ΔW X Y, Y X is perpendicular to W Z. Also, y w= w z.

To Prove: ΔW X Y ≅ ΔZ Y X

Proof:

In Δ W X Y and Z Y X

Y X ⊥ W Z→→→→Given

Y W= Y Z→→(Given)

∠YWX=∠YZX→→As, opposite sides of a triangle are equal, so angle opposite to them are equal.

∠YXW=∠YXZ→→Each being 90°

So, ΔYXW≅ΔYXZ→→[AAS]

Also, YX is common sides between two triangles.

ΔYXW≅ΔYXZ→→[HL]

So,the two triangles can be proved congruent by either AAS, or HL.