 Recall that congruent segments have the same measure.  C ONGRUENT ANGLES : Angles that have the same measure  V ERTICAL A NGLES : Nonadjacent angles formed by two intersecting lines ◦In the figure below, 1 and 2 are vertical angles ◦3 and 4 are also vertical

 T HEOREM 3-1: Vertical Angles are congruent  Examples: Find the value of x in each figure ◦ x = 1305x = 25 x = 5 ◦ x = 40 x = 135

 Some common sense theorems ◦T HEOREM 3-2: If two angles are congruent, then their complements are congruent. ◦T HEOREM 3-3: If two angles are congruent, then their supplements are congruent. ◦T HEOREM 3-4: If two angles are complementary to the same angle, then they are congruent. ◦T HEOREM 3-5: If two angles are supplementary to the same angle, then they are congruent.

 Suppose J  K and mK = 35. Find the measure of an angle that is complementary to J. ◦Because J  K, mJ = 35 ◦Complements add to 90˚, so 90 – 35 = 55˚.  In the figure below, 1 is supplementary to 2, 3 is supplementary to 2, and m1 = 50. Find m2 and m3. ◦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