Question

Select the correct answer from each drop-down menu.

∆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).

1)Pick one to go with the sentence.
a/ Triangle ABC and Triangle XYZ
b/ Triangle ABC and Triangle MNO
c/ Triangle JKL and Triangle ABC
d/ Triangle PQR and Triangle XYZ

?can be shown to be congruent by a sequence of reflections and translations.

2)Pick one to go with the sentence.
a/ Triangle ABC and Triangle XYZ
b/ Triangle PQR and Triangle XYZ
c/ Triangle JKL and Triangle PQR
d/ Triangle JKL and Triangle XYZ

?can be shown to be congruent by a single rotation.

Answer 1

Triangle ABC and Triangle XYZ can be shown to be congruent by a sequence of reflections and translations, while Triangle JKL and Triangle PQR can be shown to be congruent by a single rotation.

Step-by-step explanation:

To determine which triangles can be shown to be congruent by a sequence of reflections and translations, we need to compare the vertices of each triangle and check if they have the same coordinates. From the given options, Triangle ABC and Triangle XYZ have the same vertices at points A (11, 6) and B (5, 6). Therefore, the correct answer is a/ Triangle ABC and Triangle XYZ.

To determine which triangles can be shown to be congruent by a single rotation, we need to compare their vertices and check if they have the same coordinates after rotating one of the triangles. Triangle JKL and Triangle PQR have the same vertices at points K (12, -2) and L (12, 7), which can be obtained by rotating Triangle JKL. Therefore, the correct answer is c/ Triangle JKL and Triangle PQR.