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 1
the two triangles are related by
, so the triangles

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Explanation:

Step1: Identify Triangle Type

Both triangles are right - angled (one right angle each) and have a pair of congruent marked sides (leg) and share the right - angle. So, by the Hypotenuse - Leg (HL) or Side - Angle - Side (SAS) congruence criterion (since right angle is included between a leg and hypotenuse or between two legs), we can check congruence.

Step2: Determine Relationship and Congruence

The two triangles are related by a rotation (or transformation that maps one to the other while preserving side - angle relationships). Since we have a right angle, a congruent leg, and the hypotenuse (or another leg) relationship, using SAS (right angle is the included angle between a leg and the other side): if we consider the right angle, one congruent leg, and the hypotenuse (or the other leg which is congruent due to the right - triangle properties), the triangles are congruent. The two triangles are related by a rotation (or reflection/translation, but rotation is likely here as the orientation changes), so the triangles can be proven congruent (by SAS or HL).

Answer:

The two triangles are related by a rotation (or congruence - preserving transformation), so the triangles can be proven congruent (using SAS or HL congruence criteria as they are right - triangles with a congruent leg and right angle).