In triangle ABC and triangle PQR , BC = QR, angle A = 90 degree , angle C = angle - Maths - Congruency of Triangles

Question

In triangle ABC and triangle PQR , BC = QR, angle A = 90 degree ,
angle C = angle R = 40 degree and angle Q = 50 degree

Roopam Pandey · Accepted Answer

Dear student,I suppose here the question is to find condition of congruenceIn triangle ABC and triangle PQR,we have BC=QR                                  
1 ∠A=90° ∠C=∠R=40°                                           
2 and ∠Q=50° In triangle PQR by angle sum property we have, ∠P+∠Q+∠R=180°  ∠P+50°+40°=180°                 
 (by eqn 2)  ∠P=90°=∠A               
3 In △ABC by angle sum property we have, ∠A+∠C+∠B=180  90°+40°+∠B=180  ∠B=50°=∠Q                          
4 By eqn1,eqn3,eqn4 we get,△ABC≅△PQR         by  ASA rule of congruence  i
e angle side angle   Regards

In triangle ABC and triangle PQR , BC = QR, angle A = 90 degree , angle C = angle R = 40 degree and angle Q = 50 degree