Question

fill in the blanks:
given: \\( \overline { b d } \\) is the midsegment of the triangle.
find the values of x and y.
\\( x = \\)
\\( y = \\)

Explanation:

Step1: Use the midsegment property (length)

The midsegment \( BD \) is half the length of \( AE \). So \( 2(2x - 1)=3x + 6 \).

$$\begin{align*} 4x-2&=3x + 6\\ 4x-3x&=6 + 2\\ x&=8 \end{align*}$$

Step2: Use the midsegment property (parallel - corresponding angles)

Since \( BD\parallel AE \), \( y = 70^{\circ}\) (corresponding angles are equal).

Answer:

\(x = 8\), \(y = 70\)