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Understanding Segment and Angle Bisectors: Homework and Examples

In this week’s lesson, we explore the concepts of segment bisectors and angle bisectors. A segment bisector intersects a segment at its midpoint, while an angle bisector divides an angle into two congruent adjacent angles. We provide various examples and exercises, including finding missing angles and applying algebra to solve for unknowns. Homework consists of textbook problems that reinforce these concepts. Essential skills in geometry, such as calculating angle measures and understanding congruence, are emphasized to build a solid foundation.

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Understanding Segment and Angle Bisectors: Homework and Examples

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  1. Week 2 Warm Up 08.25.11 Circle the congruent segments and congruent angles: 2) 1)

  2. 17) ( -4, 3 ) 4) ( 1, 3 ) Homework 18) ( 1, 2 ) 5) ( 5, -7 ) 19) ( 4, 6.5 ) 6) ( 3.5, 2 ) 20) ( -5, .5 ) 21) ( -3, 3 ) 22) ( 4 , -7 ) 23) ( -0.625 , 3.5 ) 24) ( -3 , 1.5 )

  3. A segment, line, ray, or plane that intersects a segment at the midpoint. Segment Bisector • Midpoint Ex 1 C • M A B • D Bisector

  4. A ray that divides an angle in half and creates adjacent angles that are congruent Angle Bisector A • CD Bisects ∠ ACB Ex 2 • D C m∠ ACD = m ∠ DCB • B

  5. • • Find missing Angles R P S 55º Ex 3 QR Bisects ∠ PQS Q m∠PQR = m∠PQS m∠PQR = m∠RQS • 2 55º = m∠RQS 55º = m∠PQS 2 (2) 55º = m∠PQS 110º = m∠PQS

  6. Find Angle Bisector S • • R Ex 4 • Q P 70º m∡PQR = 70º = 35º 2 QS bisects ∡PQR

  7. O • Ex 5 ( 5x – 46 ) P Using Algebra ( 2x+ 5 ) • R Q OQ Bisects ∠ POR m∡POQ = m∡QOR 5x – 46 =2x + 5 • 5x - 2x- 46 = 5 3x – 46 = 5 3x = 5 + 46 3x = 51 x = 17

  8. Using Algebra x = 17 m∡POQ = 5x – 46 m∡QOR = 2x + 5 = 5( 17 ) – 46 =2( 17) + 5 = 85 – 46 =34 + 5 m∡POQ = 39º m∡QOR =39º

  9. O • R Review What is an angle bisector? P • DO 1: What is the m∡POQ? Q OQ Bisects ∠ POR • ( 3x + 16 ) ( 7x - 8 ) Assignment Textbook page 39, 34 – 54 all except # 43

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