Recall that congruent segments have the same measure.

CONGRUENT ANGLES: Angles that have the same measure

VERTICAL ANGLES: Nonadjacent angles formed by two intersecting lines◦ In the figure below, 1 and 2 are vertical angles◦ 3 and 4 are also vertical

1 23

4

THEOREM 3-1: Vertical Angles are congruent

Examples: Find the value of x in each figure

◦ x = 130 5x = 25x = 5

◦

x = 40 x = 135

Some common sense theorems◦ THEOREM 3-2: If two angles are congruent, then

their complements are congruent.◦ THEOREM 3-3: If two angles are congruent, then

their supplements are congruent.◦ THEOREM 3-4: If two angles are complementary

to the same angle, then they are congruent.◦ THEOREM 3-5: If two angles are supplementary to

the same angle, then they are congruent.

Suppose J K and mK = 35. Find the measure of an angle that is complementary to J.◦ Because J K, mJ = 35◦ Complements add to 90˚, so 90 – 35 = 55˚.

In the figure below, 1 is supplementary to 2, 3 is supplementary to 2, and m1 = 50. Find m2 and m3.◦ Since 1 and 3 are supplementary to the same angle

(2), they are congruent. Therefore, 3 = 50˚.◦ 1 and 2 are supplements, which add to 180˚, so

2 = 180 – 50 = 130˚

Two more common sense theorems:◦ THEOREM 3-6: If two angles are congruent and

supplementary, then each is a right angle. Congruent means equal Supplementary angles add to 180˚. The only equal numbers that add to 180˚ are 90˚ &

90˚.◦ THEOREM 3-7: All right angles are congruent.

All right angles are 90˚. Congruent means equal.

Assignment◦ Worksheet #3-6