Question

Someone tell me if this is right or wrong and explain it if you can! Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why JKL QRS?

Answer 1

the answer is sss, LL, HL, Sas

Answer 2

HL, LL, SSS, SAS

Explanation:

HL is the hypotenuse-leg theorem. It states that if the hypotenuse and leg of one triangle are congruent to the hypotenuse and corresponding leg of another triangle, the triangles are congruent. We have that both legs of the triangles are congruent as well as the hypotenuse, so the HL theorem applies.

LL is the leg-leg theorem. It states that if both legs of one right triangle are congruent to both legs of the second triangle, the triangles are congruent. We have that both legs are congruent; this is the LL theorem.

SSS is the side-side-side theorem. It states that if all three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. All three sides of both triangles are congruent, so this is the SSS theorem.

SAS is the side-angle-side theorem. It states that if two sides and an included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. We have JL≅QS, ∠L≅∠S and LK≅SR. This is the SAS theorem.