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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. NOV DAY Complete each congruence statement. B A D C F ABC DEF ? E Complete each congruence statement. B A ACB ECD ? C D E Complete each congruence statement. G T GHK GTK ? K H Fill in the blanks EGF BCA ____ CAB GFE ____ Complete the congruence statement. MKL JKN _____ Complete the congruence statement. ABD CBD _____ Corresponding Parts of Congruent Triangles are Congruent Fill in the blanks O If CAT DOG, then A ___ CPCTC because ________. O C D G A T Fill in the blanks RS If FJH QRS, then JH ___ Q because _______. CPCTC and F ___ If XYZ ABC, then ZX CA ___ and Y B ___ because CPCTC _______. Complete each congruence statement. If ABC DEF, then BC EF ___ Fill in the blanks If CAT DOG, thenA ___ O. Fill in the blanks BAT MON T N ___ ATB _____ ONM BA MO _____ NM 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 } 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. Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are Vertical Angles are congruent given congruent parallel lines Ex 1 SSS, SAS, ASA, AAS, HL, or not congruent. SSS SSS, SAS, ASA, AAS, HL, or not congruent. Ex 2 I AAS Ex 3 SSS, SAS, ASA, AAS, HL, or not congruent. Not congruent. Ex 4 SSS, SAS, ASA, AAS, HL, or not congruent. SAS SSS, SAS, ASA, AAS, HL, or not congruent. Ex 5 ASA 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 Ex 9 SSS, SAS, ASA, AAS, HL, or not congruent. 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? D E N L M F E N Ex 12 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? D D L L M F E N