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Lesson 1-3 Objective - To name, measure, and draw angles. Exterior A Vertex Point A B Angle Name BAC CAB Interior Sides A AB AC C Angle - Difficult to define. Formed at the intersection of two rays or line segments. B A Types of Angles Acute - Angles that measure less than 90. Obtuse - Angles that measure more than 90 and less than 180. Right - Angles that measure exactly 90. Straight - Angles that measure exactly 180. Using a Protractor to Measure Angles E C D Name the following. g One Acute Angle BEC or CEB Two Right Angles AED or DEA CED or DEC Two Obtuse Angles AEB or BEA BED or DEB One Straight Angle AEC or CEA Using a Protractor to Measure Angles Steps 1) Line up the protractor to the angle’s baseline. Using a Protractor to Measure Angles Angle Opens Right Use Inside Numbers Vertex in center of hole Steps 1) Line up the protractor to the angle’s baseline. 45 Vertex in center of hole Baseline on zero degrees Steps 1) Line up the protractor to the angle’s baseline. 2) Read the measure of the other ray. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 1 Lesson 1-3 Using a Protractor to Measure Angles Angle Opens Right Use Inside Numbers Using a Protractor to Measure Angles Angle Opens Right Use Inside Numbers 60 Angle Opens Left Use Outside Numbers Baseline on zero degrees Steps 1) Line up the protractor to the angle’s baseline. Vertex in center of hole Steps 1) Line up the protractor to the angle’s baseline. 2) Read the measure of the other ray. Draw a 37 angle that opens right. Draw a 37 angle that opens right. Steps 1) Draw baseline. Steps 1) Draw baseline. 2) Line up p protractor. 3) Mark angle. Vertex in center of hole Draw a 37 angle that opens right. Baseline on zero degrees Draw a 152 angle that opens right. Steps 1) Draw baseline. Steps 1) Draw baseline. 2) Line up p protractor. 3) Mark angle. 4) Draw ray. 5) Label angle measure. 37 If angle < 90 , it should look acute. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 2 Lesson 1-3 Draw a 152 angle that opens right. Draw a 152 angle that opens right. Steps 1) Draw baseline. Steps 1) Draw baseline. 2) Line up p protractor. 2) Line up pprotractor. 3) Mark angle. 3) Mark angle. 4) Draw ray. Vertex in center of hole Baseline on zero degrees Draw a 58 angle that opens left. Steps 1) Draw baseline. 152 If angle > 90 , it should look obtuse. 5) Label angle measure. Draw a 58 angle that opens left. Steps 1) Draw baseline. 2) Line up pprotractor. 3) Mark angle. Baseline on zero degrees Draw a 58 angle that opens left. Steps 1) Draw baseline. Vertex in center of hole Draw a 136 angle that opens left. Steps 1) Draw baseline. 2) Line up pprotractor. 3) Mark angle. 4) Draw ray. 5) Label angle measure. 58 If angle < 90 , it should look acute. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 3 Lesson 1-3 Draw a 136 angle that opens left. Draw a 136 angle that opens left. Steps 1) Draw baseline. Steps 1) Draw baseline. 2) Line up pprotractor. 2) Line up pprotractor. 3) Mark angle. 3) Mark angle. 4) Draw ray. 136 5) Label angle measure. If angle > 90 , it should look obtuse. Baseline on zero degrees Vertex in center of hole Constructing a Congruent Angle Constructing a Congruent Angle Construct X congruent to A . Construct X congruent to A . A A X X Constructing a Congruent Angle Constructing a Congruent Angle Construct X congruent to A . Construct X congruent to A . A A X X Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 4 Lesson 1-3 Constructing a Congruent Angle Construct X congruent to A . Angle Addition Postulate If N is in the interior of ABC, then mABN mNBC mABC. A N B A C If Z lies in the interior of XYK, mXYZ 45 and mZYK 80, find mXYK. mXYZ mZYK mXYK X 45 Z 45 + 80 125 80 mXYK 125 Y K X G lies in the interior of EFH. If mEFG 36 and mEFH=120, find mGFH. E mEFG mGFH mEFH G F Constructing an Angle Bisector H 36 mGFH 120 36 36 mGFH 84 Constructing an Angle Bisector Constructing an Angle Bisector Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 5 Lesson 1-3 Constructing an Angle Bisector Constructing an Angle Bisector Constructing an Angle Bisector Constructing an Angle Bisector Constructing an Angle Bisector AB bisects DAC, mDAB (5x 30), mBAC (2x 63), find mDAC. D 5x 30 B mDAB 5x 30 2x 63 5(11) 30 A C mDAB 85 mDAB mBAC (5x 30) (2x 63) mDAC 2mDAB 2x 2x 2(85) 3x 30 63 mDAC 170 30 30 3x 33 x 11 Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 6