Which congruence theorems or postulates could be given as reasons why abc =xyz

Answers: 
A) SAS
B) ASA
E) LL



Explanation:

Let's go through each possible answer choice

A. We can use SAS because we know that AC = XZ (horizontal sides) is one pair of congruent sides, the angle pairing is C = Z, and the other pair of sides is BC = YZ (vertical sides)

B. We can also use ASA. Note how A = X is one pair of angles, AC = XZ is the middle pair of sides, and C = Z is the second pair of angles. The side is between the angles.

C. We can't use SSS as we don't know AB = XY is true or not. There are no tick marks indicating congruence.

D. We can't use LA here because we don't know the altitudes (LA = leg altitude)

E. We can use LL here because we have two right triangles. The two pairs of legs (AC = XZ and BC = YZ) are congruent based on the tickmarks.

F. We can't use HL similar to the reasoning for choice C. We don't know the hypotenuses are congruent or not. If we knew that AB = XY, then we could use HL (hypotenuse leg).