2-5 PROVING ANGLES CONGRUENTObjective: to prove and apply theorems about angles

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…

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!!!

Proof of Vertical Angles Theorem

Ex 1: Using Vertical Angle Theorem

Example 1: Find the value of x. Then find the measure of each angle.

You Try…

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

Try another…

Find the values of x and y.

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….

Other useful theorems: