Rigid Motions and Congruence

Rigid Motions A rigid motion is a transformation that changes the position of a geometric figure without changing its shape or size. Examples of rigid motions include the following transformation: - Translation - Reflection - Rotation

Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts.

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

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

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

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

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 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

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 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

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

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

O because ________. CPCTC Fill in the blanks If CAT  DOG, then A  ___ because ________. CPCTC O D G C A T

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