Question

Prove that the triangle with vertices A(0,1), B(3,3), and C(3,-1) is an isosceles triangle. Select the two sides that are congruent.

Answer 1

Answer:

AB and AC are congruent

Step-by-step explanation:

To show that the triangle is isosceles, we need to show that two of the sides of the triangle are equal.

Get AB

Using the formula for calculating the distance between two points

AB = √(x2-x1)²+(y2-y1)²

A(0,1), B(3,3)

AB = √(3-0)²+(3-1)²

AB = √3²+2²

AB = √9+4

AB = √13

Get BC

B(3,3), and C(3,-1)

BC = √(3-3)²+(-1-3)²

BC = √0²+-4²

BC= √0+16

BC = √16

BC = 4

Get AC

A(0,1), and C(3,-1)

AC = √(3-0)²+(-1-1)²

AC = √3²+(-2)²

AC = √9+4

AC= √13

Since AB = AC, this shows that the triangle ABC is an isosceles triangle.

The two sides that are congruent are AB and AC