Question

Please help with this question ​

Answer 1

Answer:

Step-by-step explanation:

Given: In triangle ABC, P is the midpoint of BC. Also, PQ is parallel to CA and meets AB at point Q. QS is parallel to BC and meets AP at point R.

To prove: AP = 2AR and BC = 4QR.

Proof:

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

In triangle ABC, P is the midpoint of BC and PQ is parallel to AB. Now, by using the converse of the midpoint theorem, Q is the midpoint of AB.

In triangle ABP, Q is the midpoint of AB and QR is parallel to BP. Again, by using the converse of the midpoint theorem, R is the midpoint of AP.

So, we concluded that AP = 2AR.

For, proving the part (ii), consider triangle ABP which is having Q as the midpoint of AB and R as the midpoint of AP. Now, by using the midpoint theorem:

QR=12BP

Replacing BP as half of BC as P is the midpoint of BC, we get

QR=12(12BC)QR=14BC∴BC=4QR

So, we proved both the parts individually.