In triangle ABC, P and Q are the midpoints of sides AB and AC respectively. If BC = 14 cm, what is the length of PQ?

In triangle PQR, X is the midpoint of PQ. A line drawn through X parallel to QR meets PR at Y. If PY = 4.5 cm, what is the length of PR?

The sides of a triangle are 8 cm, 10 cm, and 12 cm. What is the perimeter of the triangle formed by joining the midpoints of its sides?

In quadrilateral ABCD, P, Q, R, and S are the midpoints of sides AB, BC, CD, and DA respectively. If AC = 16 cm and BD = 20 cm, find the perimeter of quadrilateral PQRS.

In triangle ABC, D is the midpoint of AB. The line through D parallel to BC meets AC at E. If AE = 3x - 1 and EC = 2x + 2, find the value of x.

State the Midpoint Theorem.

State the converse of the Midpoint Theorem.

In triangle LMN, P is the midpoint of LM and Q is the midpoint of LN. Prove that PQNM is a trapezium.

ABCD is a parallelogram. P and Q are the midpoints of AB and CD respectively. Prove that AQ is parallel to PC.

In triangle ABC, D is the midpoint of BC. The line through D parallel to AB meets AC at E. Prove that E is the midpoint of AC.

ABCD is a quadrilateral where the diagonals bisect each other at O. P is the midpoint of AB. Prove that PO is parallel to AD and PO=21​AD.

In triangle ABC, the median AD is produced to a point P such that AD = DP. Prove that ABPC is a parallelogram.

Prove that the quadrilateral formed by joining the midpoints of the sides of a rectangle is a rhombus.

In triangle ABC, D, E, F are the midpoints of BC, CA, AB respectively. Prove that the area of triangle DEF is one-fourth the area of triangle ABC.

In trapezium ABCD with AB || DC, P and Q are the midpoints of the non-parallel sides AD and BC respectively. Prove that PQ=21​(AB+DC).