Chapter 8.4, Problem 19PSB

Solution

To Calculate: Measure of CD

Measure of CD is $12$

Given information: $\overleftrightarrow{BE}\parallel \overleftrightarrow{CD}$ , $AB=6,BC=2,BE=9$ is provided in the question which will help to find the solution.

Formula used: Here, we are using Angle Angle similarity.

Calculation: In $\Delta BAE$ and $\Delta CAD$

  $\angle A=\angle A$ (common)

  $\angle ABE=\angle ACD$ (corresponding angles)

So, $\Delta BAE\sim \Delta CAD$ (by Angle Angle similarity)

So, $\frac{AB}{AC}=\frac{BE}{CD}$

Now, putting the values

➔ $\frac{6}{8}=\frac{9}{CD}$

➔ $CD=12$