Question

Angle b = 90 degrees, side bc = 20, angle y = 90 degrees, and side yz = 20. what additional information would you need to prove that δabc ≅ δxyz by hl? angle a is congruent to angle x. angle b is congruent to angle y. side ab is congruent to side xy. side ac is congruent to side xz.

Answer 1

D) Side AC is congruent to side XZ.

Explanation:

If triangle ABC is congruent to triangle XYZ then:

• AB = XY
• BC = YZ
• AC = XZ
• m∠A = m∠X
• m∠B = m∠Y
• m∠C = m∠Z

In triangle ABC:

• m∠B = 90°
• BC = 20

In triangle XYZ:

• m∠Y = 90°
• YZ = 20

Therefore, one of the corresponding angles is a right angle, which means both triangles are right triangles. Also, one of the corresponding legs of the two triangles is congruent.

The Hypotenuse-Leg Triangle Congruence Theorem (HL) states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the two triangles are congruent.

Therefore, to prove congruence by HL, we would need the hypotenuses of both triangles to be congruent.

The hypotenuse of a right triangle is the side opposite the right angle.

Therefore, the hypotenuses of the two triangles are:

• Hypotenuse of ΔABC = AC
• Hypotenuse of ΔXYZ = XZ

So the additional information we would need to prove that ΔABC ≅ ΔXYZ by HL is:

• Side AC is congruent to side XZ.