Without knowledge of all sides and angles, it is still possible to confirm that two triangles are comparable.
- According to the SAS criteria for triangle similarity, two sides of one triangle are comparable to two sides of another triangle if their included angles are congruent.
- According to the SAS Similarity Theorem, two triangles are similar if their respective sides are proportionate to one another and their included angles are congruent.
Given:
PQ/XY = QR/YZ and ∠Q ≅ ∠Y
To prove that, △PQR is similar to △XYZ.
Proof: 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.
To know more about angles check the below link:
brainly.com/question/25770607
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