Question

please answer fast got exam the next day seequestion in the attachment.
in the following figure, Q is the midpoint of BCand QP and QR are perpendiculars to AB andAC respectively. Also AB=AC
Prove that :
(1)ΔBPQ IS CONGRUENT TO ΔCRQ
(2)BP=CR

Answer 1

In triangle PQB & triangle RQC
BP=CR
angle P= angle R ( each 90 degree)
BQ=QC (as Q is the midpoint of BC)
By SAS congruence rule: triangle BPQ is congruent to triangle CRQ
PROVED

Answer 2

In ΔBPQ and ΔCRQ
angle P=angle R(since both are right angles given)
BQ=QC(since Q is the midpoint of BC it divides BC into equal halves)
BP=RC(since they are the parts of AB and AC and AB and AC are equal)
 
Therefore ΔBPQ is congruent to ΔCRQ by SAS congruency