Question

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21. Determine whether CD || AB. Explain your reasoning.​

Answer 1

CD is not parallel to AB

Explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, if CD is parallel to AB, then EA : AC = EB : BD.

Substitute the values of the line segments into the equation:

`\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\(28)/(20)&=(16)/(10)\\\\1.4 &\\eq 1.6\end{aligned}`

As 1.4 does not equal 1.6, then CD is not parallel to AB.

Answer 2

Answer: CD is not parallel to AB.

Reason:

If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.

Let's calculate each side separately.

• EA/EC = 28/(28+20) = 0.5833
• EB/ED = 16/(16+10) = 0.6154

Both decimal values are approximate.

The two values don't match up which makes EA/EC = EB/ED to be false.

Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.