Answer :

If the proportion of the two sides of one triangle is the same as the proportion of the two sides of another triangle, and the angle inscribed by the two sides in both triangles is equal, the triangles are said to be similar.

PQ/XY = QR/YZ and ∠Q ≅ ∠Y

We need to prove that △PQR is similar to △XYZ.

Assume PQ > XY

Draw MN parallel to BC, we find that MQN similar to XYZ

QM/QP = QN/QR --- (1)[using the basic proportionality theorem]

Now △MQN and △XYZ are congruent thus, XY/QP = YZ/QR --- (2)

Since QM = XY from (1) and (2),

XY/QP = QM/QP = QN/QR = YZ/QR

Thus, QN = YZ by SAS congruence criterion.

△MQN ≅ △XYZ

But △MQN congruent to △XYZ,

Thus, △PQR is similar to △XYZ by SAS

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Rewritten by : Barada

It is proved that △PQR is similar to △XYZ by SAS

SAS Similarity theorem states that, “If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

PQ/XY = QR/YZ and ∠Q ≅ ∠Y

We need to prove that △PQR is similar to △XYZ.

Assume PQ > XY

Draw MN parallel to BC, we find that MQN similar to XYZ

QM/QP = QN/QR --- (1)[using the basic proportionality theorem]

Now △MQN and △XYZ are congruent thus, XY/QP = YZ/QR --- (2)

Since QM = XY from (1) and (2),

XY/QP = QM/QP = QN/QR = YZ/QR

Thus, QN = YZ by SAS congruence criterion.

△MQN ≅ △XYZ

But △MQN congruent to △XYZ,

Thus, △PQR is similar to △XYZ by SAS

To learn more about similarity refer here

https://brainly.com/question/14285697

#SPJ4