Suppose, we have a transversal intersecting two parallel lines. What can be said about the corresponding angles?

Question

Homi · Accepted Answer

When a transversal cuts two parallel lines, corresponding angles are always equal.

Step 1 — Setting up the lines

Let us draw two parallel lines. We will call them line $l$ and line $m$ . Let us draw a transversal line. We will call it line $t$ . This transversal line cuts both parallel lines. It forms eight angles in total.

Diagram 1

Step 2 — Identifying corresponding angles

Corresponding angles are in the same position. They are on the same side of the transversal. One angle is outside the parallel lines. The other angle is inside the parallel lines. Let us look at our diagram. Angle 1 and Angle 5 are corresponding angles. Angle 2 and Angle 6 are corresponding angles. Angle 3 and Angle 7 are corresponding angles. Angle 4 and Angle 8 are corresponding angles.

Step 3 — Stating the property

When the two lines $l$ and $m$ are parallel, a special property holds. The corresponding angles are always equal to each other. So, we can write these equalities:

$\angle 1 = \angle 5$

$\angle 2 = \angle 6$

$\angle 3 = \angle 7$

$\angle 4 = \angle 8$

$\boxed{\text{Corresponding angles are equal}}$

Answer

(i) When a transversal intersects two parallel lines, the corresponding angles are equal.

Question 13

Answer

More questions in IT