Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
In ΔPQR and ΔXYZ, PQ=5 cm, QR=6 cm, PR=7 cm, XY=5 cm, YZ=6 cm and XZ=7 cm. Then which of the following is true?
ΔPQR\cong\triangle YXZ
ΔPQR\cong\triangle XYZ
ΔQPR\cong\triangle XYZ
ΔPRQ\cong\triangle XYZ
ΔPQR≅ΔXYZ
Match the side lengths: (5, 6, 7) in △PQR correspond to (5, 6, 7) in △XYZ such that PQ=XY, QR=YZ, and PR=XZ. Therefore, the correspondence is P↔X, Q↔Y, R↔Z.
Triangle PQR sides are PQ=5 cm, QR=6 cm, PR=7 cm. Triangle XYZ sides are XY=5 cm, YZ=6 cm, XZ=7 cm.
SSS≅SSS
Match the side lengths: (5, 6, 7) in △PQR correspond to (5, 6, 7) in △XYZ such that PQ=XY, QR=YZ, and PR=XZ. Therefore, the correspondence is P↔X, Q↔Y, R↔Z.
Confusing the order of vertices in the congruence statement; order must reflect the correspondence of equal sides.
Identify side lengths
In △PQR: PQ=5, QR=6, PR=7. In △XYZ: XY=5, YZ=6, XZ=7.
PQ=XY=5,QR=YZ=6,PR=XZ=7
Apply SSS Congruence Rule
Since all three sides of △PQR are equal to the corresponding sides of △XYZ, the triangles are congruent by the SSS (Side-Side-Side) rule.
△PQR\cong\triangle XYZ
Verify correspondence
The vertex order follows the matching sides: P connects 5 and 7, X connects 5 and 7. Q connects 5 and 6, Y connects 5 and 6. R connects 6 and 7, Z connects 6 and 7. Thus, the correct congruence is △PQR≅△XYZ.
△PQR\cong\triangle XYZ
B is correct because the sides of triangle PQR are equal to the corresponding sides of triangle XYZ in the order P-Q-R to X-Y-Z.
Congruence requires vertex order matching; always map the longest side to the longest side and smallest to smallest to confirm the correct notation.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants