Question

right triangle congruence
date 12/19/25
state if the two triangles are congruent. if they are, state how you know.
1)
2)

Explanation:

Step1: Analyze Triangle 1

In the first pair of triangles, we have a right angle (marked with the square), a pair of equal angles (marked as ∠2), and a pair of equal sides (marked with the tick). By the Angle - Angle - Side (AAS) congruence criterion (or we can also consider the Hypotenuse - Leg (HL) or other right - triangle congruence criteria after further analysis). Wait, actually, looking at the markings, we have two angles and a non - included side equal. But also, since they are right triangles, let's check the right angle (90°), one angle (∠2) and a side. Alternatively, we can see that the two triangles share some relations. Wait, maybe a better approach: For right triangles, the congruence criteria are HL (Hypotenuse - Leg), SAS, ASA, AAS. In the first diagram, we have two angles (one right angle, one ∠2) and a side equal. So by AAS, the two triangles are congruent.

Step2: Analyze Triangle 2

In the second pair of triangles, both are right triangles (right angles marked). We have two sides marked as equal (the legs with ticks). For right triangles, if the legs are equal, by the Side - Angle - Side (SAS) congruence criterion (since the included angle is the right angle, 90°), the two triangles are congruent. Also, we can think in terms of HL, but since the legs are equal, SAS is more direct here.

Answer:

1. The two triangles are congruent by AAS (or other applicable right - triangle congruence criteria).
2. The two triangles are congruent by SAS (or HL, since for right triangles with two equal legs, HL also applies as the hypotenuse can be derived to be equal from the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\) where \(a = b\) for both triangles, so hypotenuses are equal too).