Question

. Given two right angles triangles ABC and PRQ, such that ∠A = 20°, ∠Q = 20° and AC = QP. Write the correspondence if triangles are congruent. (a) ΔABC≌ ΔPQR (b) ∠ABC ≌ ΔPRQ (c) ∠ABC ≌ ΔRQP (d) ΔABC ≌ ΔQRP 8. In a triangle PQR if ∠QPR = 80° and PQ = PR, then ∠R and ∠Q are (a) 80°, 70° (b) 80°, 80° (c) 70°, 80° (d) 50°, 50°

Answer 1

Step-by-step explanation:

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Answer 2

Given : two right angles triangles ABC and PRQ, such that ∠A = 20°, ∠Q = 20° and AC = QP  

triangles are congruent.

To Find :  Write the correspondence

(a) ΔABC≌ ΔPQR (b) ∠ABC ≌ ΔPRQ (c) ∠ABC ≌ ΔRQP (d) ΔABC ≌ ΔQRP

Solution:

two right angles triangles ABC and PRQ

∠A = 20°, ∠Q = 20°

AC = QP

triangles are congruent.

Hence angle opposite to Equal side would be equal

∠B = ∠R

∠C = ∠P   ( if two angles are equal third angle also equal)

=> ΔABC ≅ ΔQRP

option  (d) ΔABC ≌ ΔQRP

In a triangle PQR  ∠QPR = 80° and PQ = PR

PQ = PR => ∠Q = ∠R

QPR = 80°  = ∠P

∠Q +  ∠R +  ∠P = 180°

=>  ∠Q +  ∠Q +  80°= 180°

=>  2∠Q = 100°

=> ∠Q =50°

∠Q = ∠R =50°

option  (d) 50°, 50°

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