Question

part 2: isosceles triangle theorem (11 - 20)
use algebra to find the missing side lengths or angles. (in an isosceles triangle, the legs and base
angles are congruent.)

1. triangle abc is isosceles with ab = ac. if ab = 3x + 4 and ac = 5x - 2, find x.
2. triangle def is isosceles with de = df. if de = 7x - 9 and df = 4x, find x.
3. triangle ghi has base angles ∠g and ∠h congruent. if m∠g = 4x + 10 and m∠h = 6x - 10, find x.
4. triangle jkl is isosceles with jl = kl. if jl = 2x + 9 and kl = 4x - 3, find x.
5. triangle mno is isosceles with vertex angle ∠m = 30° and base angles congruent. find m∠n and

m∠o.

1. triangle pqr is isosceles with pq = pr. if pq = 2x + 5 and pr = 3x - 4, find x.
2. triangle stu has base angles ∠s and ∠t congruent. if m∠s = 3x + 12 and m∠u = 90°, find m∠s

and m∠t.

1. triangle vwx is isosceles with vw = vx. if vw = 5x - 7 and vx = 2x + 8, find x.
2. triangle yza is isosceles with base angles each (4x + 10)° and vertex angle (2x + 20)°. find all

angle measures.

1. triangle bcd is isosceles with bc = cd. if bc = 7x - 8 and cd = 4x + 1, find x

Explanation:

Step1: Set up the equation

Since \(BC = CD\) in isosceles triangle \(BCD\), we set \(7x - 8=4x + 1\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(7x-4x - 8=4x-4x + 1\), which simplifies to \(3x-8 = 1\).
Add \(8\) to both sides: \(3x-8 + 8=1 + 8\), so \(3x=9\).
Divide both sides by \(3\): \(x=\frac{9}{3}=3\).

Answer:

\(x = 3\)