Question

3. In the figure below, ΔABC lies between the parallel lines.

Which property is used to prove  4 +  2 =  6?

Answer 1

It is properties of parallel lines. Here is my method in the attachment.

First, we will draw another line segment parallel to $\overline{AB}$ that passes $C$.

As alternate angles are equal by properties of parallel lines, the angle of the line subtends to $\overleftrightarrow{MN}$ is equal to $\angle4$.

Alternate angles again, we have $\angle2$ equal to the angle of the line subtending to $\overleftrightarrow{PQ}$.

As corresponding angles are equal by properties of parallel lines, 2 and 4 make the angle 6.

Hence, $\angle2+\angle4=\angle6$.

Answer 2

Given :- In the figure below, ΔABC lies between the parallel lines.

To Find :- Which property is used to prove ∠4 + ∠2 = ∠6 ?

Solution :-

In ∆ABC,

→ ∠2 + ∠4 + ∠5 = 180° { By angle sum property of a ∆. }

→ ∠2 + ∠4 = (180° - ∠5) --------- Eqn.(1)

Now,

→ ∠5 + ∠6 = 180° { Linear pair angles }

→ ∠6 = (180° - ∠5) ------------ Eqn.(2)

from Eqn.(1) and Eqn.(2),

→ ∠2 + ∠4 = ∠6

→ ∠4 + ∠2 = ∠6 (Proved)

Therefore, we can conclude that, angle sum property of a triangle is used to prove ∠4 + ∠2 = ∠6 .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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