State the property used to make the statement true. If l ∥ m , then ∠ 3 = ∠ 7

The given figure is, Here, l ∥ m and t is a transversal. From the figures ∠ 3 , ∠ 7 are the angles at the same position. These angles are formed at the corners of transversal with parallel lines. We know that, corresponding angles formed by a transversal with two parallel lines are equal. ∴ ∠ 1 = ∠ 5 Hence, the property used is corresponding angles property.

State the property used to make the statement true. If ∠ 3 = ∠ 5 , then l ∥ m

The given figure is, Here, l ∥ m and t is a transversal. From the figures ∠ 3 , ∠ 5 are the angles at the alternate interior sides. These angles are formed at the alternate sides of transversal with parallel lines. We know that, alternate interior angles formed by a transversal with two parallel lines are equal. ∴ ∠ 3 = ∠ 5 Hence, the property used is alternate interior angles property.

State the property used to make the statement true. If ∠ 3 + ∠ 6 = 180 ° , then l ∥ m

Given statement is if ∠ 3 + ∠ 6 = 180 ° , then a | | b . From the given figure, we can see that, ∠ 3 and ∠ 6 are the interior angles on the same side of the transversal. Now, if ∠ 3 + ∠ 6 = 180 ° , then a ∥ b So, if interior angles ∠ 3 and ∠ 6 are supplementary, then lines l and m are parallel. Therefore, when two lines that are intersected by a transversal line and the same-side interior angles that are formed are supplementary, or add up to 180 ° , then two lines are parallel. Hence, interior angles on the same side of the transversal are supplementary.