Question

⭐proof of converse of mid point theorem with figure .

Answer 1

Hope this helps you.

Answer 2

In the given triangle P is the mid point of AB and PQ is || to BC.

(i)

In the quadrilateral PBCR,

BP // CR

BC // PR

(ii)

In the parallelogram PBCR

BP = CR

BP = AP { P is the midpoint of AB }

CR = AP

AB || CR and AC is transversal, ∠PAQ = ∠RCQ.

AB || CR and PR is tranversal, ∠APQ = ∠CRQ

In ΔAPQ and ΔCRQ

= > CR = AP, ∠PAQ = ∠RCQ and ∠APQ = ∠CRQ

= > ΔAPQ ≅ ΔCRQ

= > AQ = CQ.

Hope this helps!