Unit 4 homework 3 isosceles and equilateral triangles answer key

Answer/Step-by-step explanation:

1. An isosceles ∆ has two equal sides. The base angles of an isosceles ∆ are also equal.

Therefore:

m<U = 54° (base angle of isosceles ∆)

m<T = 180 - (54 + 54) (sum of ∆)

m<T = 72°

2. ∆LMN is an isosceles ∆, therefore:

m<M = ½*(180 - 28) = 76°

m<N = m<M (base angle of isosceles)

m<N = 76°

3. ∆FEG is an isosceles ∆, because it has two equal base angles.

Therefore:

EF = FG

EF = 18 in

m<F = 180 - (23 + 23) = 134°

4. ∆PQR is an equilateral ∆. All sides and angles of an equilateral ∆ are equal.

Therefore:

m<P = 60°

m<Q = 60°

m<R = 60°

5. 4x + 23 = 10x - 1 (2 asides of an isosceles ∆ are equal)

Collect like terms

4x - 10x = -23 - 1

-6x = -24

Divide both sides by -6

x = 4

6. 2*(9x - 25) = 180 - 104 (base angles of isosceles ∆)

18x - 50 = 76

Add 50 to both sides

18x = 76 + 50

18x = 126

Divide both sides by 18

x = 7

7. 5x - 7 = 8x - 55 (base angles of an isosceles)

Collect like terms

5x - 8x = 7 - 55

-3x = -48

Divide both sides by -3

x = 16

8. 4x + 8 = 60° (angle of an equilateral ∆)

Subtract 8 from each side

4x = 60 - 8

4x = 52

Divide both sides by 4

x = 13

Homework 3 Isosceles And Equilateral Triangles Answers
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