Question

sss and sas congruence
state if the two triangles are congruent. if they are, state how you know.
1)
2)
name_______
date__

Explanation:

Problem 1:

Step1: Identify common side and right angles

The two triangles share a common hypotenuse (the diagonal), and both have right angles (marked with the right angle symbol). Also, the two legs adjacent to the right angles are marked as equal (the tick marks).

Step2: Apply HL (Hypotenuse - Leg) congruence criterion

For right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent. Here, the hypotenuse is common (so equal) and one leg of each right - triangle is equal (marked with tick marks). Also, we can also think in terms of SAS: the right angle is the included angle between the equal leg and the hypotenuse. The equal leg, the right angle, and the hypotenuse (common) satisfy SAS.

Step1: Identify equal sides and included angle

We can see that there is a pair of equal sides (marked with single tick marks) and a common side (the diagonal). Also, the included angle between these sides is equal (the angle between the equal side and the common side is marked as equal for both triangles).

Step2: Apply SAS congruence criterion

In SAS (Side - Angle - Side) congruence criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Here, we have two sides (one equal marked side and the common side) and the included angle between them equal for both triangles.

Answer:

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

Problem 2: