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1.5 Angle Relationships

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Adjacent Angles Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points Examples: NonExamples: B is the common Vertex is the common side

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Vertical Angles Two nonadjacent angles formed by two intersecting lines Examples: NonExamples: Vertical angles must be formed by a nice neat “X”

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Linear Pairs A pair of adjacent angles whose noncommon sides are opposite rays. Examples: NonExamples: form a straight line do not form a straight line

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Example 1

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**(These angles do not have to be connected)**

Complementary Angles Two angles whose measures have a sum of 90° Supplementary Angles Two angles whose measures have a sum of 180° (These angles do not have to be connected)

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**Example 2 Draw a picture: What do we know? Difference means subtract**

Complementary means a sum of 90° Difference means subtract Solve one equation for one of the variables: Substitute into the other equation & solve

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**Perpendicular Lines Lines that form right angles**

Perpendicular lines intersect to form 4 right angles Perpendicular lines intersect to form congruent adjacent angles Segments & rays can be perpendicular to lines or to other line segments & rays The right angle symbol in the figure indicates that the lines are perpendicular is 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

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**Example 3 90 90 Look for an equation to write & solve.**

Too many variables; look for something else 90 90 If 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.

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**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.

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Example 4

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HW : Page 41 (4– 10 all, 11 – 35 & 39 odds)

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