1. 2-5 PROVING ANGLES CONGRUENT Objective: to prove and apply theorems about angles

2. Remember… A postulate is an accepted statement of fact. A theorem is a conjecture that is proven. What is the difference between the two? You do not have to prove a postulate. You do have to prove a theorem. Let’s look at some theorems, and see how we can prove them…

3. Vertical Angles Theorem One way we can prove a theorem is by using a paragraph proof, in which we literally write the proof out as sentences in a paragraph. LET’S SEE THIS IN ACTION!!!

4. Proof of Vertical Angles Theorem

5. Ex 1: Using Vertical Angle Theorem Example 1: Find the value of x. Then find the measure of each angle.

6. You Try… You try. Find the value of x. Then find the measure of each angle.

7. Try another… Find the values of x and y.

8. Congruent Supplements Theorem In this example, x and y are both supplements of 50. Therefore,. Solve and you’ll see! The angles do not have to be vertical angles for this theorem to hold true. Look….

10. Other useful theorems: