December 2020
Intermediate to advanced
369 pages
14h 24m
English
Content preview from Pearson IIT Foundation Mathematics Class 7, 8th Edition by Pearson
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Geometry
5.55
Hints and Explanation
Let ∠A = 3x, ∠B = 4x, ∠C = 5x, and ∠D = 6x.
∴ 3x + 4x + 5x + 6x = 360°
⇒ 18x = 360°
⇒ x = 20°
∴ ∠A = 60°, ∠B = 80°, ∠C = 100°, and ∠D=120°
∴ ∠A = 60°, ∠B = 80°, ∠C = 100°, and ∠D=120°
∠A + ∠D = ∠B + ∠C = 180°
⇒
AB
is parallel to
.DC
∴ ABCD is a trapezium.
Hence, the correct option is (a).
61. Side of PQR =
12
3
= 4 cm
Given XY = 4 cm and
XY + YZ + ZX = 12 cm
⇒ YZ + ZX = 8 cm
YZ = ZX = 4 cm
∴ PQR and XYZ are congruent.
Both the triangles are similar. Option (d) follows.
Hence, the correct option is (d).
62. In ΔABC, ∠A + ∠B + ∠C = 180°.
⇒ ∠A + ∠A = 180° (given ∠A = ∠B + ∠C)
⇒ ∠A = 90°
In a right triangle ...
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