Sec. 1 – 6 Measuring Angles Objectives: 1) Find the measures of angles.

Geometry vs Algebra:

Geometry vs Algebra Segments are Congruent Symbol [ ] AB CD 1 2 Lengths of segments are equal. Symbol [ = ] AB = CD m1 = m2

Angles:

Angles Formed by 2 rays with the same endpoint Vertex of the Angle Symbol: [ ] Name it by: Its Vertex A A number 1 Or by 3 Points BAC Vertex has to be in the middle A 1 B C

Slide 4:

Ex.5: How many s can you find? Name them. 3 s ADB or BDA BDC or CDB ADC or CDA Notice D (the vertex) is always in the middle. Can’t use D But 1 or 2 could be added. A B C D 1 2

Classifying Angles by their Measures:

Classifying Angles by their Measures Acute Right Obtuse x ° x < 90 ° x ° x = 90 ° x ° x > 90 ° Straight x ° x = 180 °

Protractor Postulate:

Protractor Postulate P (1 – 7) Let OA & OB be opposite rays in a plane, & all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180. A B O D C

Angle Addition Postulate:

Angle Addition Postulate If point B is in the interior of MAD, then mMAB + mBAD = mMAD M B D A

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If MAD is a straight , then mMAB + mBAD = mMAD = 180 ° M B D A

Ex.6: Finding measures:

Ex.6: Finding measures Find m TSW if mRSW = 130 ° mRST = 100° R S T W mRST + mTSW = mRSW 100 + mTSW = 130 mTSW = 30 °

Name the angle below in four ways . The name can be the vertex of the angle: G . Finally, the name can be a point on one side , the vertex , and a point on the other side of the angle : AGC , CGA . The name can be the number between the sides of the angle: 3 . 1-4

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Use the Angle Addition Postulate to solve. m 1 + m 2 = m ABC Angle Addition Postulate. 42 + m 2 = 88 Substitute 42 for m 1 and 88 for m ABC . m 2 = 46 Subtract 42 from each side. Suppose that m 1 = 42 and m ABC = 88. Find m 2. 1-4

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Name all pairs of angles in the diagram that are: a. vertical b. supplementary Vertical angles are two angles whose sides are opposite rays. Because all the angles shown are formed by two intersecting lines, 1 and 3 are vertical angles, and 2 and 4 are vertical angles . Two angles are supplementary if the sum of their measures is 180. A straight angle has measure 180, and each pair of adjacent angles in the diagram forms a straight angle. So these pairs of angles are supplementary: 1 and 2 , 2 and 3 , 3 and 4 , and 4 and 1 .

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c. complementary Two angles are complementary if the sum of their measures is 90. No pair of angles is complementary. (continued) 1-6

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Use the diagram below. Which of the following can you conclude: 3 is a right angle, 1 and 5 are adjacent, 3 5? Although 3 appears to be a right angle, it is not marked with a right angle symbol, so you cannot conclude that 3 is a right angle. You can conclude that 1 and 5 are adjacent because they share a common side, a common vertex, and no common interior points . 3 and 5 are not marked as congruent on the diagram. Although they are opposite each other, they are not vertical angles. So you cannot conclude that 3 5.

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