Question

In the figure, ABCD is a rectangle.

P is a point on the side CD and Q

is a point on CD extended. AB = 5cm

and BC = 3 cm.

a) What is the area of the

rectangle ABCD?

b) What is the area of the triangle ∆ ABC?

c) What is the area of the triangle ∆ ABP?

d) What is the area of the triangle ∆ ABQ?

e) What is the speciality of the positions of the points C, P, and Q?​

Answer 1

Answer:

So PQRS is a rhombus.

Step-by-step explanation:

Here, we are joining A and C.

In ΔABC

P is the mid point of AB

Q is the mid point of BC

PQ∣∣AC [Line segments joining the mid points of two sides of a triangle is parallel to AC(third side) and also is half of it]

PQ=

2

1

AC

In ΔADC

R is mid point of CD

S is mid point of AD

RS∣∣AC [Line segments joining the mid points of two sides of a triangle is parallel to third side and also is half of it]

RS=

2

1

AC

So, PQ∣∣RS and PQ=RS [one pair of opposite side is parallel and equal]

In ΔAPS & ΔBPQ

AP=BP [P is the mid point of AB)

∠PAS=∠PBQ(All the angles of rectangle are 90

o

)

AS=BQ

∴ΔAPS≅ΔBPQ(SAS congruency)

∴PS=PQ

BS=PQ & PQ=RS (opposite sides of parallelogram is equal)

∴ PQ=RS=PS=RQ[All sides are equal]

∴ PQRS is a parallelogram with all sides equal

∴ So PQRS is a rhombus.