Question

4 multiple choice single... as shown in the figure, (adparallel bc). are the areas of triangle (abc) and triangle (bcd) in the figure below equal? a yes b no

Explanation:

Step1: Recall area formula for triangle

The area of a triangle is $S = \frac{1}{2}ah$, where $a$ is the base and $h$ is the height.

Step2: Analyze bases and heights of $\triangle ABC$ and $\triangle BCD$

For $\triangle ABC$ and $\triangle BCD$, they have the same base $BC$. Since $AD\parallel BC$, the distance between $AD$ and $BC$ is constant. So the height of $\triangle ABC$ and $\triangle BCD$ with base $BC$ is the same. Let the base be $BC = a$ and the height be $h$. The area of $\triangle ABC=\frac{1}{2}ah$ and the area of $\triangle BCD=\frac{1}{2}ah$.

Answer:

A. Yes