Consider right triangles ΔABC

Question

and ΔXYZ
. Angle B
and angle Y
are congruent. The hypotenuse of each triangle is AC¯¯¯¯¯¯¯¯
and XZ¯¯¯¯¯¯¯¯
, and they are congruent. What other corresponding parts must be congruent to show that ΔABC≅ΔXYZ
by the HL Congruence Theorem?
- AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

(explain why this is correct using 2 sentences and simple words)

Answer 1

To show that triangles ΔABC and ΔXYZ are congruent by the HL (Hypotenuse-Leg) Congruence Theorem, we need to prove that one of the legs of each triangle is also congruent. Since we already know the hypotenuses AC and XZ are congruent, and angles B and Y are congruent, we can conclude that the legs AB and XY must be congruent as well. This means AB ≅ XY helps complete the requirements for the HL theorem, confirming the triangles are congruent.