7 (These angles do not have to be connected) Complementary AnglesTwo angles whose measures have a sum of 90°Supplementary AnglesTwo angles whose measures have a sum of 180°(These angles do not have to be connected)
8 Example 2 Draw a picture: What do we know? Difference means subtract Complementary means a sum of 90°Difference means subtractSolve one equation for one of the variables:Substitute into the other equation & solve
9 Perpendicular Lines Lines that form right angles Perpendicular lines intersect to form 4 right anglesPerpendicular lines intersect to form congruent adjacent anglesSegments & rays can be perpendicular to lines or to other line segments & raysThe right angle symbol in the figure indicates that the lines are perpendicularis read as “is perpendicular to”(Perpendicular lines don’t form 90˚ angles; they form right angles, and right angles have a measure of 90 ˚) – this is a nit-picky fact that will be used in proofs
10 Example 3 90 90 Look for an equation to write & solve. Too many variables; look for something else9090If we want the lines to be perpendicular, they have to make right (90˚) angles.Do the solutions work?≈ means “approximately equal to” because we rounded the decimal.
11 What can you assume? Make a list of things you “think” might be true How many did you come up with? Now double check with the chart below. Mark whether each one from your list can be assumed.