BIG IDEAS: MEASUREMENT & REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: Number operations can be used to find and compare the measures of angles The Protractor.

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Presentation transcript:

BIG IDEAS: MEASUREMENT & REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: Number operations can be used to find and compare the measures of angles The Protractor and Angle Addition Postulates can be used in reasoning about angle measures MATHEMATICAL PRACTICE: Attend to precision Measuring Angles

Getting Ready Which angles below, if any, are the same size as the angle ? Describe two ways you can verify your answer.

Describe Angles An Angle is formed by two __________ with the same ____________. The rays are the ____________ of the angle. The endpoint is the ____________ of the angle. You can name an angle by: 1) its __________, 2) a point on each __________ and the ___________ which must go in the middle, 3) a __________ The interior of an angle is the region containing all the points ____________ the two sides of the angle. The exterior of an angle is the region containing all the points ____________ of the angle.

Measuring Angles The measure of an angle is related to the portion of the circle an angle takes up when the angle vertex is placed at the circle’s center. To measure the size of an angle you use degrees. Direct your eye to the ray along the straight edge of the protractor and note if the mark is in the top or bottom row of numbers. The angle’s measure is read from the same row on the scale as that Protractor Postulate: Consider Every _________ of the form can be paired ________ to ________ with a real number from ______ to ______

Types of Angles Acute angle: Obtuse angle: Right angle: Straight angle: Reflex angle:

EX 1: Name the angles, then find the measure and classify each of them. a) c) b) d)

Describing Angles Congruent angles: angles that have the ____________ measure Adjacent angles: two angles with a common _________ and ___________ but no common ____________ points Angle Addition Postulate: If C is in the ____________ of, then __________ + __________ = __________

Examples 2.Use the diagram below. Which angle is congruent to ? 3. Suppose that the angle at the right measures and that there is a point K in the interior of the angle such that. Find.

Examples 4. find x and each angle measure. 5. is a straight angle and. H is in the interior of. What is

28 Questions 1.4 p – 34 evens, 50 – 53, 62 – 78 evens