Question

PQRS is a trapezium such that PQ || SR. If M and
N are the mid-points of PQ and SR respectively
and MN is perpendicular to PQ, then which of the
following is not always true?
(1) triangle PQN is an isosceles triangle
2.PQRS is an isosceles trapezium
(3) ΔΡΝΟ is a right angled triangle
(4) triangle PSN = triangle QRN,​

Answer 1

Answer:

ΔΡΝQ is a right angled triangle is not always true

Step-by-step explanation:

M is mid point of PQ

=> PM = MQ

MN ⊥ PQ

=> PN² = PM² + MN²  

    QN²= QM² + MN²

  PM = MQ

=> PN² = QN²  => PN = QN

Δ PQN is an isosceles triangle

PQRS is an isosceles trapezium as PS = QR

as mid point creates ⊥ between Parallel lines

triangle PSN = triangle QRN

PS = QR

SN = RN   (N mid point)

PN = QN   (shown Above)

ΔΡΝQ is a right angled triangle is not always true