Question

Plzzzz help me In ΔABC, . Complete the proof showing that is parallel to .

Answer 1

AD*EB=CE*DB because cross multiplication

Answer 2

Answer: First option of STATEMENT and third option of REASON  are correct.

Step-by-step explanation:

Since we have given that

$\frac{AD}{DB}=\frac{CE}{EB}$

We need to prove that DE is parallel to AB.

For this we need to use the converse of BPT theorem.

which states that if the corresponding parts of the triangle is in same ratio, then the line joining the points of other two sides parallel to the third side.

So, we have ,

$\frac{AD}{DB}=\frac{CE}{EB}\\\\\frac{AD}{DB}+1=\frac{CE}{EB}+1(\text{ Addition property of equality)}\\\\\frac{AD+DB}{DE}=\frac{EC+EB}{EB}\\\\\frac{AB}{DB}=\frac{BC}{EB}$

Hence, First option of STATEMENT and third option of REASON  are correct.