Question

△ABC≅△DEF, BC=4x−12, and EF=−3x+16. Find x and EF.

Answer 1

x = 4 and EF = 4 ⇒ 3rd answer

Step-by-step explanation:

If two triangles are congruent, then

1. Their corresponding sides are equal

2. Their corresponding angles are equal

3. Their areas and perimeters are equal

∵ △ ABC ≅ △ DEF

∴ AB ≅ DE

∴ BC ≅ EF

∴ AC ≅ DF

∵ BC = 4 x - 12

∵ EF = -3 x + 16

∵ BC = EF

∴ 4 x - 12 = -3 x + 16

Let us solve the equation to find x

∵ 4 x - 12 = -3 x + 16

- Add 3 x for both sides

∴ 7 x - 12 = 16

- Add 12 to both sides

∴ 7 x = 28

- Divide both sides by 7

∴ x = 4

Substitute the value of x in the expression of EF

∵ EF = -3 x + 16

∵ x = 4

∴ EF = -3(4) + 16 = -12 + 16

∴ EF = 4

x = 4 and EF = 4

Learn more:

You can learn more about congruence of Δs in brainly.com/question/3202836

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