Question

In the figure ABCD is a square,M,N,O and P are the midpoints of sides AB,BC,CD and DA respectively.Identify the congreunt triangles

Answer 1

Answer:

There are 4 congreunt triangles.

Step-by-step explanation:

Given ABCD is a square.

Hence, angle A = angle B =angle C = angle D = 90.

Also, AM = MB = BN = CN = CO = OD = DP = PA

In triangle PAM and triangle MBN,

AM = BM (GIVEN)

Angle PAM = Angle MBN = 90 (GIVEN)

AP = BN (GIVEN)

Hence triangle PAM congreunt to triangle MBN by SAS congruency.

Similarly remaining triangle are also congruent by SAS criteria.

Therefore, triangle PDO, triangle PAM, triangle OCN and triangle MBN all are, congruent.