Answers:
- FG = 8.5
- GH = 11.4
- FH = 17.5
- JK = 11.4
- KL = 17.5
- JL = 8.5
- The triangles are congruent by SSS
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Explanation:
Use the distance formula to compute the length of each segment. For instance, the distance from point F to point G is the length of segment FG.
I'll show the steps on finding the length of FG
[tex]F = (x_1,y_1) = (-5,10)\\\\G = (x_2,y_2) = (-2,2)[/tex]
[tex]d = \text{distance from F to G}\\\\d = \text{length of segment FG}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-5-(-2))^2+(10-2)^2}\\\\d = \sqrt{(-5+2)^2+(10-2)^2}\\\\d = \sqrt{(-3)^2+(8)^2}\\\\d = \sqrt{9+64}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\d \approx 8.5\\\\[/tex]
The length of segment FG is approximately 8.5 units. The other side lengths are handled in the same way. As an alternative, you can use the pythagorean theorem.
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Once you determine all six lengths, note we have the following three pairs of corresponding congruent sides:
- FG = JL = 8.5
- GH = JK = 11.4
- FH = KL = 17.5
Because we have three pairs of equal sides, this means we can use the SSS (side side side) congruence theorem to prove the triangles are congruent. In other words, we have two identical triangles. One triangle is a rotated and reflected copy of the other.
The diagram is below.
