Question

∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15). ∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15). ∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7). ∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2). can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.

Answer 1

To show triangles are congruent by reflection, we show corresponding sides and angles are equal. For translation, we show corresponding sides and angles are equal. For rotation, we show corresponding angles are equal and corresponding sides have the same length.

Step-by-step explanation:

The given problem is to show that certain triangles can be shown to be congruent by a sequence of reflections and translations and can be shown to be congruent by a single rotation.

To show that two triangles are congruent by reflection, we need to show that their corresponding sides and angles are equal. To show that two triangles are congruent by translation, we need to show that their corresponding sides are equal and that their corresponding angles are equal.

To show that two triangles are congruent by rotation, we need to show that their corresponding angles are equal and that their corresponding sides have the same length.