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The HL Congruence Theorem Quick Check 1 of 51 of 5 Items Question Consider right triangles ΔABC 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?(1 point) Responses BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with bar AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper X upper Y with bar BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper X upper Z with bar AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper Y upper Z with bar Skip to navigation page 16 of 16 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

1 answer

To show that triangles ΔABC and ΔXYZ are congruent by the HL (Hypotenuse-Leg) Congruence Theorem, we already have two parts:

  1. Hypotenuses AC and XZ are congruent (AC ≅ XZ).
  2. Angle B and angle Y are congruent (∠B ≅ ∠Y).

For the HL Theorem, we need one additional pair of corresponding legs to be congruent. Since we have the hypotenuses already, we can select one of the legs as the corresponding part.

Based on the options provided, the correct third piece would be either BC or AB, provided that it corresponds correctly with the legs of the triangles. However, only one option shows the proper corresponding relationship.

The correct response to ensure that ΔABC ≅ ΔXYZ by the HL Congruence Theorem is:

BC ≅ XY

So the complete congruence matching under HL is:

  • AC ≅ XZ (hypotenuses)
  • ∠B ≅ ∠Y (angles)
  • BC ≅ XY (one pair of legs)

Thus, the triangles would be congruent.