Chapter 4 Congruent Triangles Sec 4 1 Congruent

Chapter 4 Congruent Triangles Sec. 4 – 1 Congruent Figures Objective: 1) To recognize figures & their corresponding parts

Congruent Polygons l Are the same size and the same shape. l Fit l exactly on top of each other Have corresponding parts: l Matching sides and s

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of another

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of another These are called translations and are covered in chapter 9

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of another

ΔQXT ΔPHD QX PH

Naming Polygons l Order Matters!! B C A U T W AB WU ED RS E D R ABCDE WUTSR S B U D S A W

Example: ΔWYS ΔMKV m W = 25 l m Y = 55 l Find m V l K Y 55 W 25 S M 100 V

Example 2: Congruence Statement Finish the following congruence statement: ΔJKL Δ_ _ _ M J L K N ΔJKL ΔNML

Proof: Th(4 -1) l If 2 s of one Δ are to 2 s another Δ, then the third s are also . Given: B E A D l Prove: C F l A B C D E F

Statements Reasons 1) B E & A D 1) Given 2) m B + m A + m C = 180 2) Def. of Δ m E + m D + m F = 3) 180 4) 3) m B + m A + m C = 5) m E + m D + m F 4) m B + m A + m C = 5) m B + m A + m F 5) m C = m F 6) C F 3) Trans. 4) 4) Subs. 5) Subtr. 6) Def. of

Example l Proof: G Given: GC GD CN DN Prove: ΔGCN ΔGDN C N D

G Show all of the parts are given 3 sides given reflexive C N D 3 angles given Thm 4 -1