UNIT 2 NOTE PACKET. Triangle Proofs

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1 Name GEOMETRY UNIT 2 NOTE PKET Triangle Proofs ate Page Topic Homework 9/ Vocabulary Study Vocab 9/20 4 Vocab ont. and No Homework Reflexive/ddition/Subtraction 9/ rawing onclusions from Vocab Worksheet rawing conclusions from Vocab 9/24 7 Mini Vocab Proofs No Homework 9/ QUIZ eciphering SS, S, SSS, S, HL Worksheet SSS,SS,S and S ongruence 9/26 10 Proving Triangles ongruent Geometry Practice GG28#1 9/27 11 Proving Triangles ongruent ontinued Proof Homework Worksheet 9/ PT PT Homework Worksheet 10/1 14 QUIZ No Homework Proofs W/Parallel and 2 pairs of triangles 10/2 X Proof Puzzles/ More Practice Finish Proof Puzzles 10/3 15 Isosceles Triangle Proofs No Homework 10/4 16 Overlapping Triangle Proofs Geometry Practice Sheet 10/7 X QUIZ Finish Review Sheet Review 10/8 X Review Ticket In / Study 10/9 X TEST No Homework 1

2 VOULRY UNIT 2 Term Reflexive Property- a segment or an angle is congruent to itself. (a=a) Picture/ Example Substitution Postulate- if two things are congruent to the same thing then they are congruent to each other. (If a=b and a=c then b=c) ddition Postulate- If you add the same thing to two equal things then the result is equal. (If a=b, then a+c=b+c) Subtraction Postulate- If you subtract the same thing from two equal things then the result is equal. (If a=b, then a-c=b-c) Segment isector- line that intersects a segment and cuts it into two congruent parts. ngle isector- line (or part of a line) that divides an angle into two congruent parts. Median- segment that goes from the vertex of a triangle to the MIPOINT of the opposite side. ltitude- segment that goes from the vertex of a triangle and is PERPENIULR to the opposite side. 2

3 Isosceles Triangle- triangle with exactly two congruent sides and two congruent angles. Right Triangle- triangle with a right angle. Equilateral Triangle- triangle with three congruent sides and three congruent angles. 3

4 USING REFLEXIVE/ITION/SUTRTION Reflexive property: Use REFLEXIVE when you have one part (side or angle) that is part of two triangles Example: or M E ddition postulate: Example: If and E E Then: Subtraction postulate: If Show: 4

5 rawing onclusions From Vocabulary E onclusion: Reason:_ onclusion(s): Reason: onclusion: Reason:_ onclusion: Reason:_ 5

6 onclusion: Reason:_ onclusion: H R I Reason:_ O onclusion: J H Y Reason:_ Median ltitude Intersecting lines 6

7 MINI VOULRY PROOFS 1.) Given: M is the median in Prove: M M M 2.) Given: M is the ltitude in Prove: M M M 3.) Given: N and M intersect at E Prove: and NE ME E 7

8 There are some combinations that don t work they are and! Write a congruence statement and tell which way you can tell that the triangles are congruent: 1.) 2.) 3.) 4.) 8

9 Name the additional part(s) that you would have to get congruent in order to prove that the triangles are congruent the way stated. 9

10 TRINGLE PROOFS! NOTIE~ ll of the pictures are the same and we are trying to prove the same thing each time but we will use different methods based on the givens! Make no assumptions, only draw conclusions from what you are given! 1.) Given: with bisects < Prove: 2.) Given: Isosceles triangle with is the midpoint of Prove: 3.) Given: Isosceles triangle with is the ltitude to Prove: 10

11 MORE TRINGLE PROOFS! 1.)Given: bisects Prove: E E E 2.) Given: bisects Prove: 3.) Given: and E bisect each other at Prove: E 11

12 PT P of T are Examples: You can use PT FTER you have proven two triangles are congruent to get that any additional parts are congruent! #1: HEY is congruent to MN by. What other parts of the triangles are congruent by PT? H M Y N E #2: R T, by THEREFORE:, by PT T P, by PT, by PT #3: Given: R and R Prove: 3 4 L 1 2 S 12

13 #4: Given: Prove: NLM LNO and OLN MNL M O L M O N #5 Given: and X X Prove: X 4 #6 Given: 1 2 and 3 4 Prove: XY ZW W X Z 3 Y 13

14 PROOFS WITH PRLLEL LINES N PROVING MORE THN 1 PIR OF TRINGLES ONGRUENT If you are given that two lines are parallel then you should always look for lternate Interior ngles. raw lternate interior angles: Example: 1.) Given: E bisects E Prove: E 2.) Given: E E Prove: 14

15 ISOSELES TRINGLE PROOFS Or you can do the opposite. Examples: 1.) Given: Triangle is isosceles with X is a Median to Prove: X X 2.) Given: Triangle XRY is isosceles PQ TS Q S Prove: QY SX 15

16 OVERLPPING TRINGLES PROOFS When working with overlapping triangles, try to draw the triangles separately! 1.) Given: E E Prove: 2.) Given: 1 2 E F Prove: F E 16

Geometry Rules! Chapter 4 Notes. Notes #20: Section 4.1 (Congruent Triangles) and Section 4.4 (Isosceles Triangles)

Geometry Rules! Chapter 4 Notes. Notes #20: Section 4.1 (Congruent Triangles) and Section 4.4 (Isosceles Triangles) Geometry Rules! hapter 4 Notes Notes #20: Section 4.1 (ongruent Triangles) and Section 4.4 (Isosceles Triangles) ongruent Figures orresponding Sides orresponding ngles *** parts of triangles are *** Practice: