Unit 8B EQ: What does it mean for two triangles to be congruent?

Congruent Triangles Congruent figures have the same size and same shape. The parts of congruent triangles that “match” are called corresponding parts. Two polygons are congruent if ALL pairs of corresponding parts are congruent.

ORDER MATTERS!!!! In a congruence statement Everything matches up. Informal Geometry 5/15/2018 Congruence Statement In a congruence statement ORDER MATTERS!!!! Everything matches up.

Complete each congruence statement. B A C D F DEF E

Complete each congruence statement. D B ECD

Complete each congruence statement. K G H T GTK

Fill in the blanks BCA   ____ ____   GFE EGF CAB

Complete the congruence statement. MKL _____   JKN

Complete the congruence statement. ABD _____   CBD

Corresponding Parts of Congruent Triangles are Congruent CPCTC Corresponding Parts of Congruent Triangles are Congruent

O because ________. CPCTC Fill in the blanks If CAT  DOG, then A  ___ because ________. O CPCTC O D G C A T

Q CPCTC B CPCTC Fill in the blanks If FJH  QRS, then ___ and F  ___ because _______. Q CPCTC If XYZ  ABC, then ___ and Y  ___ because _______. B CPCTC

Complete each congruence statement. If ABC  DEF, then BC  ___ EF

Fill in the blanks If CAT  DOG, then ___  O. A

BAT  MON N T  ___ _____  ONM _____  MO ATB NM  ____ BA TB Fill in the blanks BAT  MON N T  ___ _____  ONM _____  MO NM  ____ ATB BA TB

Congruent Triangles

There are 5 ways to prove triangles congruent.

Side-Side-Side (SSS) Congruence Postulate All 3 sides in one triangle are congruent to all three sides in the other triangle

Side-Angle-Side (SAS) Congruence Postulate Two sides and the INCLUDED angle (the angle is in between the 2 marked sides)

Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side (the side is in between the 2 marked angles)

Two Angles and One Side that is NOT included Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included

There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES HL

Your Only Ways To Prove Triangles Are Congruent SSS SAS ASA AAS HL HA(AAS) LL(SAS) LA (ASA) NO BAD WORDS Your Only Ways To Prove Triangles Are Congruent

There are only 3 types of markings YOU can add to a triangle if they are not already marked.

Alt Int Angles are congruent given parallel lines Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are congruent given parallel lines Vertical Angles are congruent

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 1 SSS, SAS, ASA, AAS, HL, or not congruent. SSS

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 2 I AAS

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 3 SSS, SAS, ASA, AAS, HL, or not congruent. Not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 4 SSS, SAS, ASA, AAS, HL, or not congruent. SAS

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 5 ASA

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 6 SSS, SAS, ASA, AAS, HL, or not congruent. SSS

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 7 Not congruent

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 8 SAS

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 9 SSS, SAS, ASA, AAS, HL, or not congruent. Not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent. Ex 10 SSS, SAS, ASA, AAS, HL, or not congruent. HL

Ex 11 What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N

Ex 12 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N

Worksheet Congruent Triangles #2