Proof Problem 2 Proof Using the Vertical Angles Theorem

Given: ∠ 1 ≅ ∠ 4 angle 1 approximately equal to , angle 4

Prove: ∠ 2 ≅ ∠ 3 angle 2 approximately equal to , angle 3

✓ Got It?

2. 1. Use the Vertical Angles Theorem to prove the following.

      

      Given: ∠ 1 ≅ ∠ 2 angle 1 approximately equal to , angle 2

      Prove: ∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4 angle 1 approximately equal to angle 2 approximately equal to angle 3 approximately equal to , angle 4

   2. Reasoning How can you prove ∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4 angle 1 approximately equal to angle 2 approximately equal to angle 3 approximately equal to angle 4  without using the Vertical Angles Theorem? Explain.

Take Note: Theorem 2-2 Congruent Supplements

Theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

If …

∠ 1 angle 1  and ∠ 3 angle 3  are supplements and ∠ 2 angle 2  and ∠ 3 angle 3  are supplements

Then …

∠ 1 ≅ ∠ 2 angle 1 approximately equal to , angle 2

You will prove Theorem 2-2 in Problem 3.