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SB Geom 14 Completed.notebook September 13, 2012 Lesson 1.4 Measure and Classify Angles angle consists of two different rays with the same endpoint sides of the angle rays with common endpoints D vertex the endpoint B To name an angle: use the vertex if only two rays use three points with vertex in the middle A C Example 1. Name three angles. Aug 248:26 AM Postulate 3. Protractor Postulate Consider OB and a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180. Measure of <AOB is the absolute value of the difference between the real numbers for OA and OB. Classifying Angles Acute an angle with a measure greater than zero and less than 90 Right an angle with a ninety degree angle Obtuse an angle with a measure greater than 90 and less than 180 Straight an angle with a measure with 180 degrees Aug 248:33 AM 1 SB Geom 14 Completed.notebook September 13, 2012 How to measure angles with a protractor. 123oo 123 36o Aug 248:38 AM Example 2. Find the angle measure. a. <KHJ b. <GHK c. <GHJ d. <GHL Guided Practice. 1. Name all the angles in the diagram at the right. Which angle is a right angle? 2. Draw a pair of opposite rays. What type of angle do the rays form? Aug 248:43 AM 2 SB Geom 14 Completed.notebook September 13, 2012 Postulate 4. Angle Addition Postulate If P is the interior of <RST, then the measure of <RST is equal to the sum of the measures of <RSP and <PST. R m<RST = m<RSP + m<PST S P T Example 3. m<LKN = 145 o, find m<LKM and m<MKN. Aug 248:46 AM Aug 248:56 AM 3 SB Geom 14 Completed.notebook September 13, 2012 congruent angles two angles with the same measure m<A = m<B <A ≅ <B Aug 248:58 AM 5. Identify all pairs of congruent angles in the diagram. 6. In the diagram, m<PQR = 130 o, m<QRS = 84 o, and m<TSR = 121 o. Find the other angle measures in the diagram. angle bisector a ray that divides an angle into two congruent angles A B D BD bisects <ABC so <ABD ≅ <DBC C Aug 249:01 AM 4 SB Geom 14 Completed.notebook September 13, 2012 Example 5. In the diagram at the right, VW bisects <XYZ, and m<XYW = 18 o. Find m<XYZ. 7. AC bisects <ABD. Find m<BAC and m<CAD. 4x 10 2x +30 Aug 249:06 AM Homework Lesson 1-4 2-60 Evens Aug 249:09 AM 5