Question

The following pairs of triangles are congruent? Give reasons

Answer 1

Answer:

Step-by-step explanation:

In ΔABC and ΔPQR

∠ABC = ∠PQR      (Each 90°)

AC = PR                 ( BY P.G.T.)

BC = PQ                 (Given in fig.)

                                                      HENCE PROVED

Answer 2

ΔABC and ΔRQP can be shown congruent using Pythagorean theorem

ΔABC ≅ Δ RQP    (Using SSS)

Pythagorean theorem:

Square on the hypotenuse of a right-angled triangle is

equal to the sum of the squares of the other two perpendicular sides.

in ΔABC

AC² = AB² + BC²

=> AC² = 8² + 6²

=> AC² = 64 + 36

=> AC² = 100

=> AC = 10 cm

in ΔPQR

PQ² + QR² = PR²

=> 6² + QR² = 10²

=> QR = 8 cm

in ΔABC and ΔPQR

AB ≅ QR   ( 8 cm)

BC ≅ PQ   (6 cm)

AC ≅ PR    (10 cm)

ΔABC ≅ Δ RQP    (Using SSS)

Hence shown that given pairs of triangles are congruent