Let ABC, PQR be two congruent triangles such that angle A = angle P = 90°. If BC = 13cm, PR = 5cm, find AB.

To find the length of AB in triangle ABC, which is congruent to triangle PQR, we can use the properties of right triangles.

Given:

– Triangle ABC is a right triangle with angle A = 90°.

– BC = 13 cm (hypotenuse).

– Triangle PQR is also a right triangle with angle P = 90° and PR = 5 cm (hypotenuse).

Since triangles ABC and PQR are congruent, it means all corresponding sides and angles are equal.

Thus, if PR = 5 cm, BC in triangle ABC must also correspond to the hypotenuse of triangle PQR. Given that BC = 13 cm, we can use the Pythagorean theorem to solve for AB.

In triangle ABC:

[ AB^2 + AC^2 = BC^2 ]

Let ( AC = x ). Since PR is also given to be equal to the corresponding sides of triangle ABC (which means corresponding sides in congruent triangles are equal):

– Let ( PQ = AB ) and ( QR = AC ).

– Therefore, ( AB ) corresponds to ( PR = 5 ) cm.

Now we have:

1. ( BC^2 = AB^2 + AC^2 )

[ 13^2 = AB^2 + AC^2 ]

[ 169 = AB^2 + AC^2 ]

2. Using the fact that ( AC ) corresponds to