4.1 4.2 Congruency

Congruency: Congruent figures ____________________________ __________________________________________ ______________________________________________________________________________________________________________________________ Angles Sides D A B C E F

In a proof, if triangles are congruent and you plan to prove that corresponding pieces are congruent use: __ __ __ __ __ __________________________________________

Reasons for Proving Triangles Congruent Postulate 12: ____________________________ __________________________________________

Postulate 13: _____________________________ ________________________________________

Postulate 14:_______________________________ __________________________________________

O M T K

A Y Z 1 2 3 4 B

4.3 Proving other Congruencies

M 1 3 J K 2 4 O

D C 1 2 A B

C B A D

M J k 1 2 3 4 L

M J k 1 2 3 4 L

R S O P Q

B A E D C

4.4 Isosceles Triangles

Lets draw an Isosceles Triangle

Def of Isosceles Triangle: _______________________________________ Theorem 4-1: ___________________________________ __________________________________________________ Theorem 4-2:________________________________ ___________________________________________ ______________________________________________________________________________________

Corollary 2: _________________________________ __________________________________________

Examples: x 4x-6 16 50 18 X=_______ X=_______

4.5 Triangles Congruent

More Ways to Prove Triangles Congruent Theorem 4.3:_______________________________ __________________________________________

Theorem 4.4:_______________________________ __________________________________________

Examples: x 21 21 4x-1 3x+3 65 19-x X=_______ X=_______

L P x Q 1 4 2 3 70 M N X=________

Z Y A B C

4.6 Proving More than one set of Triangles Congruent

D O C A B

D O X C A B

X D 1 C 2 A O B

4.7 Altitude, Median and Perpendicular Bisector

Median: ________________________________ _________________________________________ ___________________________________ A C B

Altitude: ____________________________ _____________________________________ ____________________________________ Acute Right Obtuse

Perpendicular Bisector ___________________ ________________________________________ _______________________________________

PBT –___________________________________ ________________________________________ C A B

CPBT –_________________________________ ________________________________________ C A B

Theorem 4.7: _______________________ _____________________________________

D O C B

D O C B