Question

prove that BC=1/2 QR​

Answer 1

Given:

• AQ || BC
• AR || BC
• AC || BQ
• AB || RC

To prove:

⟶ BC = 1/2 QR

Proof:

First let's understand the concept.

Concept used:

→ If 2 pairs of sides are parallel in a quadrilateral, then the quadrilateral is a parallelogram.

→ Opposite sides are equal in a parallelogram.

In Quadrilateral ACBQ,

AC || BQ and AQ || BC.

So, ACBQ is a parallelogram.

We know that;

Opposite sides of a parallelogram are equal.

∴ QA = BC   → → → [Equation 1]

_____________________________________

In Quadrilateral ABCR,

BC || AR and AB || RC

So, ABCR is a parallelogram.

We know that;

Opposite sides of a parallelogram are equal.

∴ AR = BC  → → → [Equation 2]

Equating Equation 1 and 2,

${\large{\bf{QA = AR = \dfrac{1}{2} QR \qquad \dashrightarrow \sf{[Equation~ 3]}}}}$

From Equation 1,

QA = BC

Substitute BC instead of QA in Equation 3

$\therefore \large{\boxed{\bf{\large{BC = \dfrac{1}{2} QR}}}}$

★ Hence Proved ★