ACC Math 1 EQ: What does it mean for two triangles to be congruent?

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.

In a congruence statement ORDER MATTERS!!!! Everything matches up.

Complete each congruence statement. CA E D B F DEF

ECD C A E D B Complete each congruence statement.

GTK K G H T Complete each congruence statement.

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

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

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

Corresponding Parts of Congruent Triangles are Congruent

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

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

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

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

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

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)

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

Your Only Ways To Prove Triangles Are Congruent NO BAD WORDS

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

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

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

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

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

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

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

Ex 6 SSS

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

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

Ex 9 Not congruent.

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