Session 6 Daily Check 1) and are midsegments of the triangle. Find the length of RT and UW. (2 points each) 2) Use the Triangle Proportionality Theorem to solve for x. (3 points each) a) b)

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Homework Review

CCGPS Analytic Geometry Day 6 ( ) UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13 Today’s Question: What does it mean for two triangles to be congruent? Standard: MCC9-12.G.SRT5, CO.7-8

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Complete each congruence statement. CA E D B F DEF

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? ECD C A E D B Complete each congruence statement.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? GTK K G H T Complete each congruence statement.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Corresponding Parts of Congruent Triangles are Congruent

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Fill in the blanks If  CAT   DOG, then  A  ___ because ________. OO CPCTC C A T O D G

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Fill in the blanks If  FJH   QRS, then ___ and  F  ___ because _______. QQ CPCTC BB If  XYZ   ABC, then ___ and  Y  ___ because _______.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

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

Before we start…let’s get a few things straight AB C XZ Y INCLUDED ANGLE

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

Ex 1 DFEUVW by ____ SSS

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S Y X Z ΔRST  ΔYZX by SSS Ex 2

Not congruent. Not enough Information to Tell R T S B A C Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Ex 3

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Ex 4 R P S Q ΔPQS  ΔPRS by SAS

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Ex 5 R P S Q ΔPQR  ΔSTU by SSS T U

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Ex 6 N M R Not congruent. Not enough Information to Tell Q P

Before we start…let’s get a few things straight INCLUDED SIDE AB C XZ Y

Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side

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

Your Only Ways To Prove Triangles Are Congruent NO BAD WORDS

Ex 1 DEFNLM by ____ ASA

Ex 2 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 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N

Determine whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. ΔGIH  ΔJIK by AAS G I H J K Ex 4

ΔABC  ΔEDC by ASA BA C ED Ex 5 Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔACB  ΔECD by SAS B A C E D Ex 6 Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Not possible K J L T U Ex 7 Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. V

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?