in the diagram below MNPQ is a parallelogram whose diagonals are perpendicular prove M & PQ is a rhombus

Given : MNPQ is a parallelogram whose diagonals are perpendicular.

To prove :  MNPQ is a rhombus.

Proof:

In parallelogram MNPQ,

R is the intersection point of the diagonals MP and NQ( shown in below diagram)

(Because, the diagonals of parallelogram bisects each other)

(Right angles )

 (Reflexive)

Thus, By SAS postulate of congruence,

By CPCTC,

Similarly,

We can prove,

By CPCTC,

But, By the definition of parallelogram,

and

⇒

All four side of parallelogram MNQP are congruent.

⇒ Parallelogram MNPQ is a rhombus.

Hence, proved.

Given : MNPQ is a parallelogram whose diagonals are perpendicular.

To prove :  MNPQ is a rhombus.

Proof:

In parallelogram MNPQ,

R is the intersection point of the diagonals MP and NQ( shown in below diagram)

(Because, the diagonals of parallelogram bisects each other)

(Right angles )

 (Reflexive)

Thus, By SAS postulate of congruence,

By CPCTC,

Similarly,

We can prove,

By CPCTC,

But, By the definition of parallelogram,

and

⇒

All four side of parallelogram MNQP are congruent.

⇒ Parallelogram MNPQ is a rhombus.

Hence, proved.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The answer is in the image 

The answer is in the image 

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales