Which property proves triangles are congruentttt

a. Length of RS = √26 Units

b. Length of SP = √50 Units

c. Length of PQ = √26 units

d. Length of RQ = √50 Units

e. Yes , it is a parallelogram.

Step-by-step explanation:

Given,

P(2 , 2) , Q(1 , -3 ) , R( -4 , 2 ) , S( -3 , 7 )

Now,

To find the length of RS, SP , PQ and RQ , we have to use the formula of distance:

Finding the length of RS

R ( -4 , 2) ---> (X1 , y1 )

S( -3 , 7 ) ----> ( x2 , y2 )

RS=

The length of RS = √26 Units

b. Finding the length of SP

S( -3 , 7)----> (X1 , y1 )

P ( 2 , 2 ) ----> ( x2 , y2 )

SP =

The length of SP is √50 units.

c. Finding the length of PQ

P( 2 , 2 ) ------> (x1 , y1 )

Q ( 1 , -3 ) ------> (x2 , y2 )

PQ=

The length of PQ is √26 units

D. Finding the length of RQ

R( -4 , 2 )----> (X1 , y1 )

Q( 1 , -3 )------> (x2 , y2)

RQ=

The length of RQ = √50 units

e. Determining whether the quadrilateral is a parallelogram or not.

Please see the attached picture

Opposite sides are equal.

Now,

P( 2 , 2 )----> (x1 , y1 )

R( -4 , 2 )----> (x2 , y2 )

PR ( Diagonal)

again,

S ( -3 , 7)----> (X1 , y1 )

Q ( 1 , -3)-----> ( x2 , y2)

Diagonals are not equal.

So, it is a parallelogram.

Hope this helps...

Good luck on your assignment...