Question

post test: polygons
a
x m
d
4 m
c
6 m
8 m
a. 3 m
b. 2 m
c. 5 m
d. 4 m

Explanation:

Step1: Apply the angle - bisector theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. In \(\triangle ABC\), assume the line from the top vertex to point \(D\) is the angle - bisector of the angle at the top vertex. Then \(\frac{AB}{AC}=\frac{BD}{DC}\). Here, we can also use the property of similar - looking triangles formed by the angle - bisector. We have \(\frac{6}{8}=\frac{x}{4}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying the proportion \(\frac{6}{8}=\frac{x}{4}\) gives us \(8x = 6\times4\).

Step3: Simplify the right - hand side

\(6\times4=24\), so the equation becomes \(8x = 24\).

Step4: Solve for \(x\)

Dividing both sides of the equation \(8x = 24\) by 8, we get \(x=\frac{24}{8}=3\).

Answer:

A. 3 m