Question

You know that two triangles have the same interior angles, but you’re not sure whether they’re congruent. The first triangle has coordinates (0, 0), (3, 0), and (0, 4). The second triangle has coordinates (2, -1), (2, 3), and (-1, -1). Use the distance formula to find the length of all three sides determine whether the triangles are congruent.

Answer 1

The triangles are congruent.

Explanations:

The formula for calculating the distance between two points is expressed as

D = √(x₁ - x₂)²+(y₁ - y₂)²

For the first triangle with coordinates A(0, 0), B(3, 0), and C(0, 4).

Find the measure of the sides:

AB = √(3- 0)²

AB = √9

AB = 3

BC = √(4)²+(-3)²

BC = √25

BC = 5

AC = √(4- 0)²

AC = 4

For the other three coordinates (second triangles)

The second triangle has coordinates D(2, -1), E(2, 3), and F(-1, -1).

DE = √(3+1)²+(2-2)²

DE = √16

DE = 4

EF = √(-1-3)²+(-1-2)²

EF = √(-4)²+(-3)²

EF = √25

EF = 5

DF = √(-1-2)²+(-1+1)²

DF = √(-3)²

DF = 3

Note that for the first triangle to be congruent to the second triangle, the measure of their hypotenuse sides must be equal.

Since they are both right angled triangle and the measure of their hypotenuse (longest side) is equal that is BC = EF, hence the triangles are congruent.