5 1 Reteach Perpendicular and Angle Bisectors Continued
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1 -5 Segment and Angles Bisectors Warm Up Lesson Presentation Lesson Quiz Holt Geometry
1 -5 Segments and Angles Bisectors Warm Up 1. Draw AB and AC, where A, B, and C are noncollinear. Possible answer: A B C 2. Draw opposite rays DE and DF. F Solve each equation. 3. 2 x + 3 + x – 4 + 3 x – 5 = 180 31 4. 5 x + 2 = 8 x – 10 4 D E
1 -5 Segments and Angles Bisectors Objectives Bisect a Segment. Bisect and Angle
1 -5 Segments and Angles Bisectors Vocabulary Midpoint Segment Bisector Straightedge Construction Angle Bisector Bisects Compass Construct Midpoint Formula
1 -5 Segments and Angles Bisectors A segment can be divided into two identical parts using the Midpoint. In geometry we say that the midpoint bisects a segment if it is equidistant from the endpoints. An segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint.
1 -5 Segments and Angles Bisectors Activity 1: Construct Segment Bisector
1 -5 Segments and Angles Bisectors If you know the coordinates of the endpoints of a segment, you can find the coordinates of the midpoint by using the Midpoint Formula:
1 -4 Angles 1 -5 Segments and Their Angles Measures Bisectors Example 1: Using the Midpoint Formula
1 -4 Angles 1 -5 Segments and Their Angles Measures Bisectors Example 1: Using the Midpoint Formula
1 -5 Segments and Angles Bisectors An Angle Bisector is a ray that divides and angle into two adjacent angles that are congruent.
1 -5 Segments and Angles Bisectors Activity 1: Construct Angle Bisector
1 -5 Segments and Angles Bisectors Example 2: Using Angle Bisectors If you know the measure of the bigger angle, we can use the definition of angle bisectors to find the measure of the smaller angles.
1 -5 Segments and Angles Bisectors Example 2: Using Angle Bisectors
1 -5 Segments and Angles Bisectors Example 3: Using the Angle Addition Postulate m DEG = 115°, and EF is the angle bisector. Find m FEG m DEG = m DEF + m FEG 115 = 2(m FEG) 115 2 57. 5 = m FEG Angle Additions Postulate. Equality property. Divide by 2 on both sides. Simplify.
1 -5 Segments and Angles Bisectors Check It Out! Example 3 m XWZ = 121° and m XWY = 59°. Find m YWZ = m XWZ – m XWY Add. Post. m YWZ = 121 – 59 Substitute the given values. m YWZ = 62 Subtract.
1 -5 Segments and Angles Bisectors Example 4: Finding the Measure of an Angle KM bisects JKL, m JKM = (4 x + 6)°, and m MKL = (7 x – 12)°. Find m JKM.
1 -5 Segments and Angles Bisectors Example 4 Continued Step 1 Find x. m JKM = m MKL Def. of bisector (4 x + 6)° = (7 x – 12)° +12 Substitute the given values. 4 x + 18 – 4 x = 7 x – 4 x 18 = 3 x 6=x Add 12 to both sides. Simplify. Subtract 4 x from both sides. Divide both sides by 3. Simplify.
1 -5 Segments and Angles Bisectors Example 4 Continued Step 2 Find m JKM = 4 x + 6 = 4(6) + 6 Substitute 6 for x. = 30 Simplify.
1 -5 Segments and Angles Bisectors Check It Out! Example 4 a Find the measure of each angle. QS bisects PQR, m PQS = (5 y – 1)°, and m PQR = (8 y + 12)°. Find m PQS. Step 1 Find y. Def. of bisector Substitute the given values. 5 y – 1 = 4 y + 6 y– 1=6 y=7 Simplify. Subtract 4 y from both sides. Add 1 to both sides.
1 -5 Segments and Angles Bisectors Check It Out! Example 4 a Continued Step 2 Find m PQS = 5 y – 1 = 5(7) – 1 Substitute 7 for y. = 34 Simplify.
1 -5 Segments and Angles Bisectors Check It Out! Example 4 b 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 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 -5 Segments and Angles Bisectors Check It Out! Example 4 b Continued 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° Simplify.
1 -5 Segments and Angles Bisectors Lesson Quiz: Part I Classify each angle as acute, right, or obtuse. 1. XTS acute 2. WTU right 3. K is in the interior of LMN, m LMK =52°, and m KMN = 12°. Find m LMN. 64°
1 -5 Segments and Angles Bisectors Lesson Quiz: Part II 4. BD bisects ABC, m ABD = , and m DBC = (y + 4)°. Find m ABC. 32° 5. Use a protractor to draw an angle with a measure of 165°.
1 -5 Segments and Angles Bisectors Lesson Quiz: Part III 6. m WYZ = (2 x – 5)° and m XYW = (3 x + 10)°. Find the value of x. 35
1 -5 Segments and Angles Bisectors Skills Autonomous Practice Pages: 29, 30, 31, 32
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