recall that congruent segments have the same measure. c ongruent angles : angles that have the same...
TRANSCRIPT
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