Question

Choose one of the following theorems and prove it: Vertical Angles are congruent, Alternate interior angles are congruent, Corresponding angles are congruent. Demonstrate on a whiteboard

Answer 1

By prove of theorem, It is true that Vertical angles are congruent.

Using theorem to prove that Vertical angles are congruent.

Vertical angles are created during the joining or intersecting of two lines at a point. When this occur, we generate four angles with two of pairs vertical angles also know as nonadjacent angles.

From the image attached below, the two pairs of vertical angles are:

• (∠1, ∠3)
• (∠2, ∠4)

Proof:

If the sum of all the angles on a straight line = 180 degrees.

Then, we can infer that:

∠1 + ∠2 = 180°

∠1 + ∠4 = 180°

Using the transitive property, we can then say:

∠1 + ∠2 = ∠1 + ∠4

Removing ∠1 on both sides, we have:

∠2 = ∠4

Since this same rule is also applicable to ∠1 = ∠3.

Therefore, we can conclude that it is true that Vertical angles are congruent.