Which Is Different? Are △ PQR and △ TSR the same size and shape? Answers: See solution.
Practice makes perfect
We want to determine which of the given questions is different. Let's read them!
First, let's recall that a dilation is a type of transformation in which a figure is made smaller or larger with respect to a point called the center of dilation. Notice that a scale drawing is an example of a dilation. This means that two out of the four questions ask about the same thing.
Next, let's recall that a similarity transformation is a dilation or a sequence of dilations and rigid motions. Therefore, if two figures are similar, then one of them is a dilation or a scale drawing of the other one.
This means that the only question that is different is whether △ PQR and △ TSR are the same size and shape. Now, let's take a look at the given diagram.
We can see that △ PQR and △ TSR are the same shape but they are not the same size. Next, sides TS and PQ are parallel and both are intersected by side RQ. Therefore, ∠ TSR and ∠ PQR are congruent, corresponding angles.
Additionally, both triangles share ∠ R. This means that two angles in △ PQR are congruent to two angles in △ TSR, so the third angles are also congruent. Therefore, △ PQR and △ TSR are similar. We can also say that △ PQR is a dilation or a scale drawing of △ TSR.
