Question

the quadrilateral PQRS. The sides PQ and Rs are Parallel 'x' is the midpoint of Q R the lines sx and pq extended meet y

(I) are the area of triangle spx and triangle qyx equal? why?​

Answer 1

Answer:

the quadrilateral PQRS. The sides PQ and Rs are Parallel 'x' is the midpoint of Q R the lines sx and pq extended meet y

Answer 2

Step-by-step explanation:

Given :-

The quadrilateral PQRS. The sides PQ and RS are Parallel 'x' is the midpoint of QR, the lines SX and PQ extended meet y .

To find :-

Are the area of ∆SRX and ∆QYX equal? why?

Solution :-

Given that

PQRS is a quadrilateral.

PQ || RS

X is the mid point of QR and SX

The lines SX and PQ extended meet y .

Now,

In ∆ SRX and ∆QYX

SX = XQ ( X is the mid point )

<SXR = QXY (Vertically Opposite angles)

<SRX = <YQX ( PQ || RS , QR is a transversal , alternative interior angles)

By ASA Property

∆ SRX is congruent to ∆ QYX

=> ∆SRX =~ ∆QYX

=> area (∆SRX ) = area (∆QYX)

Since the areas of two congruent triangles are equal.

Answer:-

The area of ∆SRX and the area of ∆QYX are equal.

Used formulae:-

If two parallel lines Intersected by a transversal then,

→ Vertically Opposite angles are equal.

→ Alternative interior angles are equal.

→ Areas of two congruent triangles are equal.