Congruence and triangles Chapter 4 Section 4.2 Congruence and triangles

Warm-Up

Congruent Figures Two geometric figures are congruent if the have exactly the same size and shape When figures are congruent Corresponding angles are congruent Corresponding sides are congruent Yes, all corresponding parts are  Are these two  ?

Writing congruence statements When writing a congruence statement it is important that the pieces correspond in the statement just like in the picture.

A M T C D N

T 48 5 cm 73 JTM

Third Angle Theorem If two angles of a triangle are congruent to two angles of another triangle, then the third angles are also congruent A  D and B  E thus C  F

Proving Figures Are Congruent To prove two geometric figures congruent Must show all corresponding angles are  Must show all corresponding sides are 

Determine If the Figures Can Be Proven Congruent Given DEG  FGE Given D  F Right Angle Thm DGE  FEG Third Angle Theorem Reflexive Yes DGE  FEG Def.  ’s

Determine If the Figures Can Be Proven Congruent Given N  R Given P  T M  Q No ’s not 

Determine If the Figures Can Be Proven Congruent Given X  Z Given XYW  ZYW Right Angle Thm XWY  ZWY Third Angle Theorem Reflexive Yes XYW  ZYW Def.  ’s

Use the given information to find the values of x and y

Use the given information to find the values of a and b mT = 6(9) – 3 = 51 mT + mR + mS = 180 51 + 83 + mS = 180 mS + 134 = 180 mS = 46 6a – 3 = 51 6a = 54 a = 9 7b – 10 = 46 7b = 56 b = 8