Using the given coordinates, calculate the lengths of the triangle's three sides.
The triangles are congruent.
Practice makes perfect
We want to determine whether triangles ABC and DEF are congruent. To do so, let's start by drawing the two triangles on the coordinate plane.
According to the Side-Side-Side Congruence Theorem, if three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. To determine if this is the case for our triangles, let's find the lengths of the sides.
Vertical and Horizontal Sides
To find the lengths of the vertical and horizontal sides, we can check the changes in the x- and y-values between the vertices.
As we can see, AB=DE and BC=EF. This means that these sides are congruent.
AB ≅ DE and BC ≅ EF
Diagonal Sides
To calculate the length of the third side, we can use the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Distance
AC
( - 2, - 2), ( 4,6)
sqrt(( - 2- 4)^2+( - 2- 6)^2)
10
DF
( 13,1), ( 5,7)
sqrt(( 13- 5)^2+( 1- 7)^2)
10
The third sides of the triangles also have the same length. Therefore, we can claim that the triangles are congruent by the Side-Side-Side Congruence Theorem.
