determine if ΔFGH and ΔJKL are congruent. If they are give the reason if they aren't choose "not congruent". F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)

Question

enter them to the nearest tenth. Plz help me. I really need to answer this in a time limit of 15 minutes.

Answer 1

DISTANCE FORMULA: d = square root of [(x₂ - x₁)² + (y₂ - y₁)²]

The question asks if the 2 triangles, FGH & JKL, are congruent. For this question, we can use the DISTANCE FORMULA to find the length of all 3 sides of both triangles. Let's do that.

1st - Segment FG - F(-5,10) and G(-2,2)

d = square root of [(-2 - (-5))² + (2 - 10)²] = square root of [(-2 + 5))² + (-8)²] = √[3² + (-8)²]

d = √(9 + 64) = √73 -----> Segment/side FG has a length of √73

2nd - Segment GH - G(-2,2) H(-9,-7)

d = square root of [(-9 - (-2))² + (-7 - 2)²] = √[(-7)² + (-9)²] = √(49 + 81)√= √130

Segment/side GH has a length of √130

3rd - Segment HF - H(-9,-7) & F(-5,10)

d = square root of [(-5 - (-9))² + (10 - (-7))²] = √(4² + 17²) = √(16 + 289) = √305

Using the same methods to find the lengths of all 3 sides of triangle JKL, we find that JK = √130; KL = √305; and LJ = √73

FG ≅ LJ - GH ≅ JK - HF ≅ KL

Because the 2 triangles have the same 3 side lengths, they are congruent triangles.