Question

in triangle abc and pqr BC is equals to QR is equals to 6 CM Angle A is equals to 90 degree angle b is equals to angle q is equals to 50 degree and angle r is equals to 40 degree is ABC Triangle congruent to Triangle pqr​

Answer 1

Answer:

yes, triangle ABC is congruent to triangle PQR

Step-by-step explanation:

Given : angle B is congruent to angle Q...... (50 degree each) .....(equation 1)

also, side BC is congruent to side QR........ (6cm each)....... (equation 2)

angle A = 90 degree ......(equation 3)

angle R = 40 degree

Solution: let's find angle p

therefore, in triangle PQR

angle Q = 50 degree......... (given)

angle R = 40 degree......... (given)

therefore, in triangle PQR

by angle sum property of triangle

angle P + angle Q + angle R =180 degree

angle P + 50 degree + 40 degree = 180 degree

angle P + 90 degree = 180 degree

angle P = 180 degree - 90 degree

angle P = 90 degree .........( equation 4)

Now we can say that :

In triangle ABC and triangle PQR

angle A is congruent to angle P ............( by equation 3 and 4)

angle B is congruent to angle Q ...........( by equation 1 )

side BC is congruent to side QR......... ( by equation 2)

thus, triangle ABC is congruent to triangle PQR by AAS ( Angle Angle Side) test of congruency .