1. Complete the congruence statement. ABC  ____ DFE Warm – up: 5 minutes 1. Complete the congruence statement. ABC  ____ DFE A B C F E D 2. If CDE  TUV. mT = 32, and mV = 83, find mD. 65 3. Find the slope of (-2, -5) and (-4, -10). 5/2

Review Yesterday we learned about Congruent Triangles. What does it mean if 2 triangles are congruent? What VERY IMPORTANT abbreviation did we learn yesterday? What does it mean?

4.4 SSS and SAS

Slash marks: indicate congruence, and angle markings Slash marks: indicate congruence, and angle markings. You must follow the markings!

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

Angles can have different measures! 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. Angles can have different measures!

Ex 1 Determine if 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

Side-Angle-Side (SAS) Congruence Postulate Two sides are congruent and the INCLUDED angle.

Angle in between two consecutive sides X Z Y INCLUDED ANGLE

ΔPQS  ΔPRS by SAS Ex 2 P R Q S Determine if 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

Ex 3 DFE UVW by ____ SSS

Not enough Information to Tell Ex 4 Determine if 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

ΔPQR  ΔSTU by SSS Ex 5 P S U Q R T Determine if 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 if 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

4.5 ASA , AAS, AND HL

The side between 2 angles C X Z Y INCLUDED SIDE

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

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

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

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 4 G I H J K ΔGIH  ΔJIK by AAS

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 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 K L M ΔJMK  ΔLKM by SAS or 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 8 J T L K V U Not possible

WORK workbook

PRACTICE Worksheet Proofs