and are midsegments of the triangle. Session 6 Daily Check 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)
Homework Review Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
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
5-4 Congruent Triangles 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. B A C D F DEF E Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Complete each congruence statement. D B ECD Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Complete each congruence statement. K G H T GTK Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Corresponding Parts of Congruent Triangles are Congruent CPCTC Corresponding Parts of Congruent Triangles are Congruent Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
O because ________. CPCTC Fill in the blanks If CAT DOG, then A ___ because ________. O CPCTC O D G C A T Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
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 Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Congruence of Triangles Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
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
Before we start…let’s get a few things straight C X Z Y INCLUDED ANGLE
Side-Side-Side (SSS) Congruence Postulate 4 4 5 5 6 6 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 DFE UVW by ____ SSS
Ex 2 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
Not enough Information to Tell Ex 3 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S B A C Not congruent. Not enough Information to Tell
ΔPQS ΔPRS by SAS Ex 4 P R Q S Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R Q S ΔPQS ΔPRS by SAS
ΔPQR ΔSTU by SSS Ex 5 P S U Q R T Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S U Q R T ΔPQR ΔSTU by SSS
Not enough Information to Tell Ex 6 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R Q N Not congruent. Not enough Information to Tell
Before we start…let’s get a few things straight C X Z Y INCLUDED SIDE
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
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 NO BAD WORDS Your Only Ways To Prove Triangles Are Congruent
Ex 1 DEF NLM 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. Ex 4 G I H J K ΔGIH ΔJIK by AAS
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. B A C E D Ex 5 ΔABC ΔEDC by ASA
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. Ex 6 E A C B D ΔACB ΔECD by SAS
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. Ex 7 J T L K V U Not possible