Question

7. In APQR, ZQ = 90°. QM is the median of the
triangle through Q. Prove that QM =1/2 PR.​

Answer 1

Answer:

QM is median to hypotenuse PR, Hence it is half of the PR. Because triangle PQR is right angle triangle.

Step-by-step explanation:

Given QM is median

Hence, PM = MR

Constructed MN median to triangle QMR

Hence, QN = NR

MN is mid segment so

MN || PQ

Corresponding angles in two parallel lines intersected by a transversal line QN

angle PQR = angle MNR = 90° as PQR is right angle triangle and

Angle PQR and angle MNR are congruent angles

So MNR =90°

Angle MNQ = 180°- MNR = 180°-90° = 90°

MNR=MNQ

MN=MN common side

So TRIANGLE MNQ = triangle MNR - - - Side angle side postulate

QM = MR, Corresponding sides in congruent triangles

MR = (1/2)PR, as QM is median to hypotenuse

So

QM = (1/2)PR