Question

The vertices of a triangle are P(-1, 3), Q(2, -1), and R(5, 3).

Choose all of the congruent sides of the triangle.

PQ
PR
QR

Answer 1

the answer is PQ and QR

Answer 2

Ok so to find which sides are congruent we need to know their lengths.

To find the length we need the distance formula between two point ->

√(X2-X1)∧2 +(Y2-Y1)∧2

Ok lets find the first side PQ

P(-1,3) Q(2,-1)
X1 Y1 X2 Y2

√(2-(-1)∧2 + (-1-3)∧2 = 5

Now PR

P (-1,3) R (5,3)
X1 Y1 X2 Y2

√(5-(-1))∧2 + (3-3)∧2) = 6

Now the last side QR

Q (2, -1) R (5,3)
X1 Y1 X2 Y2

√(5-2)∧2 + (3-(-1))∧2 = 5

From the above work we see that PQ and QR are congruent becuase they are equal PQ=QR

Also the opposite angles of these sides are congruent. Hope this helps :).