Question

In ΔXYZ and ΔEFG, angles Y and F are right angles. Which set of congruence criteria would be enough to establish that the two triangles are congruent by HL?

Answer 1

XZ ≅ EG and YZ ≅ FG is enough to make triangles to be congruent by HL. Option b is correct.

Two triangles ΔXYZ and ΔEFG, are given with Y and F are right angles.

Condition to be determined that proves triangles to be congruent by HL.

What is HL of triangle?

HL implies the hypotenuse and leg pair of the right-angle triangle.

Here, two right-angle triangles ΔXYZ and ΔEFG are congruent by HL only if their hypotenuse and one leg are equal, i.e. XZ ≅ EG and YZ ≅ FG respectively.

Thus, XZ ≅ EG and YZ ≅ FG are enough to make triangles congruent by HL.

Learn more about HL here:

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In ΔXYZ and ΔEFG, angles Y and F are right angles. Which set of congruence criteria would be enough to establish that the two triangles are congruent by HL?

A.

XZ ≅ EG and ∠X ≅ ∠E

B.

XZ ≅ EG and YZ ≅ FG

C.

XZ ≅ FG and ∠X ≅ ∠E

D.

XY ≅ EF and YZ ≅ FG