1 / 15

Understanding Geometric Proofs: Key Steps in Congruence and Segment Bisectors

This resource outlines fundamental concepts in geometry, focusing on segment bisectors, medians, altitudes, and important theorems related to angle bisectors. It provides a structured approach to proving congruence using methods such as SAS, ASA, and SSS, alongside crucial definitions and properties of geometric figures. Engage with practice problems to solidify understanding of concepts such as perpendicular bisectors and congruency of angles. This guide will help students navigate through various proofs and enhance their geometric reasoning skills.

aggie
Télécharger la présentation

Understanding Geometric Proofs: Key Steps in Congruence and Segment Bisectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related