1 3 Measuring and Constructing Angles Objectives Students

1 -3 Measuring and Constructing Angles Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition Postulate 3, How to use angle bisector. . Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Vocabulary Do you know? Angle Vertex Measure Degree Interior of an Angle Exterior of an Angle Acute Angle Obtuse Angle Right Angle Straight Angle Congruent Angle Angle Bisector Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Name the Angles Name each angle in three or more ways. 1. 2. 3. Name three different angles in the figure. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Classify the Angles Use the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse. a. BOA m BOA = 40° BOA is acute. b. DOB m DOB = 125° DOB is obtuse. c. EOC m EOC = 105° EOC is obtuse. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Congruent angles are angles that have the same measure. Arc marks are used to show that the two angles are congruent. m ABC = m DEF, so you can write ABC DEF. This is read as “angle ABC is congruent to angle DEF. ” Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles angle bisector An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 1: Using the Angle Addition Postulate m DEG = 115°, and m DEF = 48°. Find m FEG m DEG = m DEF + m FEG Add. Post. Substitute the given values. Subtract 48 from both sides. Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Check it Out: Example 1 m XWZ = 121° and m XWY = 59°. Find m YWZ. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 2: Finding the Measure of an Angle KM bisects JKL, m JKM = (4 x + 6)°, and m MKL = (7 x – 12)°. Find m JKM. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 2 Continued Step 1 Find x. m JKM = m MKL Def. of bisector Substitute the given values. Add 12 to both sides. Simplify. Subtract 4 x from both sides. Divide both sides by 3. Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 2 Continued Step 2 Find m JKM. Substitute 6 for x. Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Check It Out! Example 2 Find the measure of each angle. JK bisects LJM, m LJK = (-10 x + 3)°, and m KJM = (–x + 21)°. Find m LJM. Step 1 Find x. LJK = KJM (– 10 x + 3)° = (–x + 21)° +x +x – 9 x + 3 = 21 – 3 – 9 x = 18 x = – 2 Holt Mc. Dougal Geometry Def. of bisector Substitute the given values. Add x to both sides. Simplify. Subtract 3 from both sides. Divide both sides by – 9. Simplify.

1 -3 Measuring and Constructing Angles Check It Out! Example 2 Step 2 Find m LJM = m LJK + m KJM = (– 10 x + 3)° + (–x + 21)° = – 10(– 2) + 3 – (– 2) + 21 Substitute – 2 for x. = 20 + 3 + 21 = 46° Holt Mc. Dougal Geometry Simplify.

1 -3 Measuring and Constructing Angles Lesson Quiz: Do you understand the lesson? Independent Practice Textbook pg 24 #8 and 9 Challenge: pg 25 # 30 ~~~~~~~~~~~~~~~~~ Homework: 1. 3 Handout – will be given out once textbook work is checked. Holt Mc. Dougal Geometry