Question

Use the figure to answer the questions.

(a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.

(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain.

Answer 1

Part (a) answer: segment AC is congruent to segment JL

Part (b) answer: segment BC congruent to segment KL

Explanation:

(a) SAS is side-angle-side

You know that angle A and angle J are right angles, so they are congruent. You also know sides AB and JK are congruent. That gives you side-angle. You need side-angle-side, so you need the next pair of corresponding sides, so you need sides AC and JL

Part (a) answer: segment AC is congruent to segment JL

(b) HL is hypotenuse-leg

Becasue both triangles have a right angle, they are right triangles. Sides AB and JK are congruent corresponding legs of two right triangles. To use the HL theorem, you need a pair of congruent legs, which you already have, and the hypotenuses must be congruent.

Part (b) answer: segment BC congruent to segment KL