Question

In ∆ ABC and ∆ PQR, BC=QR, angle A= 90° , angle C = angle R=40° and angle Q = 50 ° . Find the triangles congruent and also state the condition of congruency.

Answer 1

the triangle is congruent by ASA congruency that is angle side angle
angle a = angle p =90°
angle b = angle q = 50°
angle c= angle r = 40°

Answer 2

In triangle ABC and triangle PQR,we have
BC=QR......................................................1
angleA=90°
angleC=angleR=40°...............................2
and angleQ=50°
In triangle PQR by angle sum property we have,
angleP+angleQ+angleR=180°

anglep+50°+40°=180° (by eq2)

angleP=90°=angleA...........................3
In triangleABC by angle sum property we have,
angleA+angleC+angleB=180

90°+40°+angleB=180

angleB=50°=angleQ...........................4
By eq1,eq3,eq4 we get,
tringleABC congruent to triangle PQR by
ASA criterion rule i.e angle side angle.