11/7 - isosceles and equilateral practice
find the values of x and y.
11/7 - isosceles and equilateral practice
find the values of x and y.

Question

Accepted Answer

# Explanation:
## Step1: Find $ x $
In $\triangle ABD$ and $\triangle CBD$, $AB = CB$, $BD=BD$, $AD = CD = 2$ (given). So, $\triangle ABD\cong\triangle CBD$ (by SSS - Side - Side - Side congruence criterion). Then $\angle ABD=\angle CBD=x$.
In $\triangle ABD$, using the angle - sum property of a triangle ($\angle A+\angle ABD+\angle ADB = 180^{\circ}$). But since $\triangle ABD\cong\triangle CBD$, and for $\triangle ABC$ (isosceles with $AB = CB$), $\angle A=55^{\circ}$.
The sum of angles in $\triangle ABC$: $\angle A+\angle ABC+\angle C=180^{\circ}$. Also, $\angle ABC = 2x$ and $\angle A=\angle C = 55^{\circ}$ (base angles of isosceles triangle $ABC$).
$$
\begin{align*}
55^{\circ}+2x + 55^{\circ}&=180^{\circ}\
2x&=180^{\circ}-(55^{\circ}+ 55^{\circ})\
2x&=70^{\circ}\
x& = 35^{\circ}
\end{align*}
$$
## Step2: Find $ y $
Since $AD = CD = 2$ (given), $\triangle BCD$ (or $\triangle ABD$) is isosceles. But also, from the congruence $\triangle ABD\cong\triangle CBD$, and using the side - length property. $y = 2$ (because $AD = CD$ and $AD = 2$)

# Answer:
$x = 35$, $y = 2$

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Question

Explanation:

Step1: Find \( x \)

Step2: Find \( y \)

Answer: