Question

In Fig. 12.44,
XZ = QZ = 5
cm, angle Y = 100°.
angle XZY = 50° and
angle PQZ = 30°.
Prove that:
(a) triangle XYZ ~= triangle QPZ
(b) XY = PQ​

Answer 1

Answer:

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Answer 2

in ΔXYZ

∠x= 30° [angle sum property of triangle]

Similalrly,

∠QZP=50° [ vertically opposite angle of ∠YZX]

Therefore, ∠P=100°

in ΔXYZ and ΔQPZ

∠Q = ∠X = 30° {ANGLE }

XZ = QZ [ GIVEN ] { SIDE }

∠X = ∠P = 100°

∴ ΔXYZ≅ΔQPZ [ ASA ]

⇒ By CPCT XY=PQ