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Warm-Up—Find the Key Steps

Warm-Up—Find the Key Steps. Prove AB = CD A) B) C) D). X. O. D. C. A. B. Y. ANSWER TO 4-6 Side #1 #2. Definition of Segment Bisector Vertical Angles are Congruent SAS CPCTC Vertical Angles are Congruent ASA CPCTC. SSS CPCTC Vert. Angles are Congruent ASA CPCTC

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Warm-Up—Find the Key Steps

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  1. Warm-Up—Find the Key Steps Prove AB = CD A) B) C) D) X O D C A B Y

  2. ANSWER TO 4-6 Side #1 #2 Definition of Segment Bisector Vertical Angles are Congruent SAS CPCTC Vertical Angles are Congruent ASA CPCTC SSS CPCTC Vert. Angles are Congruent ASA CPCTC Supps to congruent angles are congruent #3 ASA

  3. Answers to 4-3 Side #1 1)Given 2)Vert. Angles cong. 3) SAS 4) CPCTC #2 1) Given 2) Corr. Angles are cong. 3) ASA 4) CPCTC 5) corr. angles cong, then parallel #3 1) Given 2) Def of mdpt. 3) Reflexive 4) SSS 5) CPCTC 6) Def of <bisector

  4. 4-7 Medians, Altitudes, and Perpendicular Bisectors

  5. Median • A segment from a vertex to the midpoint of the opposite side. • Median—Midpoint--Middle

  6. Altitude A perpendicular segment from a vertex to the opposite side. Makes a 90 and comes from the vertex. Acute Right Obtuse This leg is the altitude

  7. Perpendicular Bisector • A segment/ ray/ line that is perpendicular to the segment at its midpoint. • Combo: 90 AND Midpt • Only one with 2 words and has 2 things to look for

  8. THEOREM 3-5 • If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. SP ____ PA P● S● ●A

  9. THEOREM 3-6 (CONVERSE OF 3-5) • If a point is equidistant from the endpoints of the segment, then it is on the __________________________ of the segment. perpendicular bisector

  10. THEOREM 3-7 • If a point lies on the bisector of an angle, then it is equidistant from the __________ of the angle. If BP bisects <B, then ______=______ . If MP = PN, then P lies on the ____________________ of <B. • Converse: If a point is equidistant from the sides of an angle, then it lies on the ________ _____________ of the angle. sides A● A● A● A● A● A● MP PN M● P ● C ● C ● C ● N B B B B B B B B angle bisector angle bisector

  11. Practice 1. Given: P is on the perpendicular bisector of XY. P is equidistant from _____ and _____. 2. If P is equidistant from ______ and ______, then ______=_______ . P ● X● ●Y M X Y X Y XM MY

  12. Practice 3. If P is on the angle bisector of <DEF, then P is equidistant from ______ and _____. D● P● ● F E

  13. Practice 4. If LN bisects <JLK, then N is equidistant from ______ and ______ . 5. If O is the midpoint of LK and JO LK , then: a) P is equidistant from ____ and _____. b) and JO is the _____________________ of LK. L LJ LK O P● M L K J K N perpendicular bisector

  14. Practice 6. If ,then KM is a(n) _____________ of JKL. 7. If LO = OK, then JO is a (an) ____________ of JKL. 8. If P is equidistant from K and L, then P is on the _____________________ of LK. 9. If O is equidistant from JL and JK , then O is on the _____________________ of <J. altitude L median O P● perpendicular bisector M J K N angle bisector

  15. Homework Worksheet 4-7

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