Question

Borderline

Your late grandfather left you and your cousin his property in his will. Below is a map of the
property with a road that cuts through the property
North Property Border
Road
South Property Border
1. On the diagram, two angles (<1 und 2) formed by the road, and the borders are congruent.
What is the relationship
between the north and south property borders of your prandfather's
land?
Explain how you know
2. How are <3 and <1 related to each other
Explain how you know

Answer 1

1. The North and South property border lines are parallel

2. ∠3 and ∠1 are supplementary angles

Explanation:

The given parameters are;

The North and South Property Boarders are given

The road intersects (transverses) the North and South Property Boarders

∠1 and ∠2 in the given diagram are congruent

1. Given that ∠1 ≅ ∠2, and from the diagram, ∠1 and ∠2 are alternate interior angles, we have that alternate interior formed by the transversal of two parallel lines are congruent

Therefore, the North and South property border lines are parallel

2. ∠3 and ∠1 are same side interior angles

When two parallel lines have a common transversal passing through them, then the same side interior angles are supplementary

Therefore, ∠3 and ∠1 are supplementary (angles whose sum is 180°)

The proof is that ∠3 and ∠2 are supplementary, because they are the angles on a straight line

∠2 ≅ ∠1 which is given

∴ ∠2 = ∠1 by definition of congruency

∠3 and ∠1 are therefore, supplementary, by substitution property of equality