Question

kuta software - infinite geometry
sss and sas congruence
state if the two triangles are congruent. if they are,
1)

Explanation:

Step1: Identify given information

We have two right triangles. They share a common hypotenuse (the diagonal side), and the legs with tick marks are congruent (marked with two ticks), and both are right - angled triangles (right angles are marked).

Step2: Apply congruence criterion

For right - angled triangles, we can also use the Hypotenuse - Leg (HL) congruence criterion, but we can also analyze using SAS. Let's consider the right angles, the congruent legs, and the common hypotenuse. The right angle is an included angle between the leg (with ticks) and the hypotenuse.
In triangle 1 (left) and triangle 2 (right):

• One leg of each triangle (the ones with two tick marks) is congruent.
• The hypotenuse is common, so it is congruent for both triangles.
• Both triangles are right - angled, so the angle between the congruent leg and the hypotenuse is a right angle (90 degrees) and is congruent for both triangles.

By the SAS (Side - Angle - Side) congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Here, the two sides are the congruent leg (with ticks) and the hypotenuse, and the included angle is the right angle. So the two triangles are congruent by SAS (or HL, which is a special case of SAS for right - angled triangles).

Answer:

The two triangles are congruent (by SAS or HL congruence criterion).