40 42 Warm up Solve for the variable. 1. 2. 4x – 20 x 2y + 28

Congruent Triangles

Congruent triangles have 3 congruent sides and 3 congruent angles. Informal Geometry 12/2/2018 Congruent Triangles Congruent triangles have 3 congruent sides and 3 congruent angles. The parts of congruent triangles that “match” are called corresponding parts.

ORDER MATTERS!!!! In a congruence statement Everything matches up. Informal Geometry 12/2/2018 Congruence Statement In a congruence statement ORDER MATTERS!!!! Everything matches up.

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

Complete each congruence statement. B If ABC  DEF, then BC  ___ EF A C D F E

Complete each congruence statement. B If ABC  DEF, then A  ___ D A C D F E

Complete each congruence statement. B If ABC  DEF, then C  ___ F A C D F E

Fill in the blanks If CAT  DOG, then AC  ___ OD

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

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

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

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

5 ways to Prove Triangles Congruent

Side-Side-Side (SSS) Congruence Postulate All Three 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 A S A S 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…Hypotenuse Leg HL

Your Only Ways To Prove Triangles Are Congruent SSS SAS ASA AAS HL NO BAD WORDS Your Only Ways To Prove Triangles Are Congruent

4 markings YOU can add if they aren’t marked already

Share a side Vertical Angles Reason: Reflexive Property Reason: Vertical Angles are congruent

Alternate Interior Angles Reason: Alt. Int angles are congruent

Opposite congruent sides are congruent angles. Isosceles Triangle Opposite congruent sides are congruent angles.