Using the given coordinates, calculate the length of the triangle's three sides.
Yes, they are congruent.
Practice makes perfect
Let's start by drawing the two triangles on a 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 it is the case, let's first find the lengths of the sides.
Horizontal Sides
Since two sides are horizontal, we can find their lengths from the graph by checking the difference between x-coordinates of the vertices.
We can see that the length of both sides is 9. This means that AC ≅ DF.
Diagonal Sides
To calculate the lenghts of the diagonal sides, we can use the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Length
AB
( 0,0),( 6,5)
sqrt(( 6- 0)^2+( 5- 0)^2)
sqrt(61)
BC
( 6,5),( 9,0)
sqrt(( 9- 6)^2+( 0- 5)^2)
sqrt(34)
DE
( 0,-1),( 6,-6)
sqrt(( 6- 0)^2+( -6-( -1))^2)
sqrt(61)
EF
( 6,-6),( 9,-1)
sqrt(( 9- 6)^2+( -1-( -6))^2)
sqrt(34)
We found that the diagonal sides also have the same length. Therefore, AB≅DE and BC≅EF. Since all three corresponding sides are congruent, we can claim that the triangles are congruent by the Side-Side-Side Congruence Theorem.
