Question

Based only on the information given in the diagram, which congruence

theorems or postulates could be given as reasons why Hij is congruent to klm

Answer 1

The correct answer is HA and AAS.

Explanation:

The HA (hypotenuse angle) states "if the hypotenuse and one acute angle of a right triangle are congruent to the hypotenuse an done acute angle of another triangle, then the triangles are congruent.

The AAS (angle-angle-side) theorem states "If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the triangles are congruent.

Answer 2

C. HA

D. AAS

Explanation:

∆HIJ is a right triangle with a given labelled acute angle and a given hypotenuse, which are congruent to the acute angle and hypotenuse length of ∆KLM, by on the Hypotenuse-Acute Angle Theorem (HA), ∆HIJ and ∆KLM are congruent.

Also, the two triangles have two given angles that are congruent, and a non-included side (hypotenuse), which are congruent in both triangles, by definition of the AAS congruency theorem, both triangles can be said to be congruent.

Therefore, the congruency theorems that could be given as reasons why both triangles are congruent to each other are the HA and AAS theorems.