Question

PQR is a triangle right angled at Q. A line through the midpoint M of the hypotenuse PR and parallel to RC intersects PQ at D. Show that;

D is the midpoint of AC.

MD ⊥ PQ

​

Answer 1

Answer:

(1) M is the mid point of AB and

MD∥BC

D is the mid point of AC

(2) As MD∥BC &

AC is transversal

∠MDC+∠BCD=180

∘

∠MDC+90

∘

=180

∘

⇒∠MDC=90

∘

⇒MD⊥AC

(3) In △AMD and △CMD

AD=CD

∠ADM=∠CDM

DM=DM

△AMD≅△CMD

AM=CM⇒AM=

2

1

AB⇒CM=AM