Question

Based only on the information given in the diagram, which congruencetheorems or postulates could be given as reasons why ACDE=A OPQ?Check all that apply.СA. ASAB. HAC. SASD. LLE. HLF. AAS

Answer 1

The postulates of congruence for right triangles are

• Hypotenuse-Leg Theorem.

,

• Leg-Leg Theorem.

,

• Leg-Acute Angle Theorem.

,

• Hypotenuse-Acute Angle Theorem.

In this case, we know that sides CE and OQ are congruent. (hypotenuses are congruent)

Angle C is congruent to angle O.

Angle E is congruent to angle Q.

To demonstrate the congruence between triangles we can use Hypotenuse-Acute Angle Theorem since they are congruent between triangles.

We can also use Hypotenuse-Leg Theorem because we have corresponding legs and hypotenuses congruent.

The hypotenuse-acute angle theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of acute angles congruent.

The hypotenuse-leg theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of congruent legs.

Therefore, the right choices are B and E.