Question

question
determine the relationship between the two triangles and whether or not they can be proven to be congruent.
answer attempt 1 out of 2
the two triangles are related by , so the triangles

Explanation:

Step1: Analyze the triangles

Both triangles are right - angled (have a right angle). Also, the legs (the sides forming the right angle) of one triangle are equal to the legs of the other triangle (marked as equal in the figure).

Step2: Apply the congruence criterion

The Side - Angle - Side (SAS) congruence criterion for right - angled triangles (where the angle is the right angle) states that if the two legs of one right - angled triangle are equal to the two legs of another right - angled triangle, the triangles are congruent. Here, we can also use the Hypotenuse - Leg (HL) criterion. First, since the legs are equal, by Pythagoras' theorem \(c=\sqrt{a^{2}+b^{2}}\), the hypotenuses (where \(a\) and \(b\) are the legs) of the two right - angled triangles are equal. For right - angled triangles, if the hypotenuse and a leg (here the legs are equal, and we can consider one leg and the hypotenuse) are equal, the triangles are congruent.

Answer:

The two triangles are related by congruence, so the triangles are congruent (by the Hypotenuse - Leg (HL) or Side - Angle - Side (SAS) criterion for right - angled triangles).