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
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Explanation:

Step1: Analyze triangle properties

Both triangles are right - angled (have a right angle, \(90^{\circ}\)). They also have two sides marked as equal (congruent) in length. The transformation that relates them is a rotation (since one can be rotated to match the other's orientation). For congruence, we can use the Hypotenuse - Leg (HL) theorem for right - angled triangles or Side - Angle - Side (SAS) congruence criterion. Since they are right - angled, have one leg equal and the hypotenuse equal (or we can consider the two sides and the included right angle), they are congruent.

Step2: Determine the relationship and congruence

The two triangles are related by a rotation (a type of rigid transformation). Rigid transformations (rotation, reflection, translation) preserve the size and shape of the figure, so if two figures are related by a rigid transformation, they are congruent. Also, using the SAS congruence criterion: in right - angled triangles, we have a right angle (equal), one leg equal (marked), and the hypotenuse (the side opposite the right angle) can be shown to be equal (since the other leg is also equal, by Pythagoras \(c=\sqrt{a^{2}+b^{2}}\), if \(a\) and \(b\) are equal for both triangles, \(c\) will be equal). So the triangles are congruent.

Answer:

The two triangles are related by a rotation (or rigid transformation), so the triangles can be proven to be congruent.