Question

exit ticket: mapping triangle pqr onto pqr these figures are congruent. describe the rigid transformation(s) that map triangle pqr onto triangle pqr. explain how you know the two triangles are congruent. justify.

Explanation:

Step1: Identify the transformation type

By observing the position of Triangle PQR and Triangle P'Q'R', we can see that it is a translation. To find the translation vector, we compare the coordinates of corresponding vertices. Let's take vertex P(1,1) and P'(5,1).

Step2: Calculate the translation vector

The x - coordinate of P' is 5 and of P is 1, so the horizontal displacement $\Delta x=5 - 1=4$. The y - coordinates of P and P' are the same (y = 1), so the vertical displacement $\Delta y=0$. The translation vector is $\langle4,0
angle$.

Step3: Justify congruence

Since a translation is a rigid - motion, it preserves distance and angle measures. For two triangles, if we can map one onto the other using a rigid - motion (in this case, translation), the corresponding sides and angles are congruent. By the definition of congruent triangles (if all corresponding sides and angles are congruent, the triangles are congruent), Triangle PQR and Triangle P'Q'R' are congruent.

Answer:

The rigid transformation that maps Triangle PQR onto Triangle P'Q'R' is a translation by the vector $\langle4,0
angle$. The two triangles are congruent because translation is a rigid - motion that preserves side lengths and angle measures.