Question

determine the relationship between the two triangles and whether or not they can be proven to be congruent.
answer
the two triangles are related by , so the triangles

Explanation:

Step1: Analyze the triangle type

The triangle shown is a right triangle (has a right angle). We have two legs marked as equal (the tick marks) and the right angle is common or corresponding? Wait, actually, for right triangles, the Hypotenuse - Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. But also, if we have two legs equal (marked) and the right angle (which is included between the two legs), so Side - Angle - Side (SAS) because we have two sides (the legs) and the included angle (the right angle) equal. Wait, but let's check the markings. The triangle has a right angle, and two legs with tick marks (so those sides are congruent), and the included angle (the right angle) is congruent. So SAS: two sides and the included angle. Alternatively, HL is for hypotenuse and leg, but here we have two legs. Wait, maybe the triangle is a right triangle, and we have two legs congruent and the right angle. So SAS: Side (leg), Angle (right angle), Side (other leg). So the relationship is SAS, and since SAS is a congruence criterion, the triangles can be proven congruent. Wait, but let's confirm. The options include HL, SAS, etc. Let's see: the triangle has a right angle, and two legs (the sides forming the right angle) are marked as congruent. So that's two sides (legs) and the included angle (right angle), so SAS. So the first blank is SAS, and the triangles can be proven congruent.

Step1: Identify the congruence criterion

Looking at the triangle: it's a right triangle with two legs (sides) marked as congruent and the included right angle. This matches the Side - Angle - Side (SAS) criterion (two sides and the included angle are congruent).

Step2: Determine congruence

Since SAS is a valid triangle congruence criterion, the two triangles (assuming the other triangle has corresponding parts) can be proven congruent.

Answer:

The two triangles are related by \(\boldsymbol{\text{Side - Angle - Side (SAS)}}\), so the triangles \(\boldsymbol{\text{can be proven to be congruent}}\).