ccgps analytic geometry (8-19-13)

CCGPS Analytic Geometry(8-19-13)

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

? ABC DEF

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

? ACB ECD

C

A

ED

B

Complete each congruence statement.

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

? GHK GTK

KG

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

CPCTCC

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 CPCTC

J H RS

B CPCTCIf XYZ ABC, then ___ and Y ___ because _______.

ZX CA

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 congruen

t

Alt Int Angles are congruent

given parallel

lines

Before we start…let’s get a few things straight

A B

C

X Z

Y

INCLUDED ANGLE

Side-Side-Side (SSS) Congruence Postulate

66

4 45 5

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

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 1

Ex 2

statement. congruence a Write.

and , , trianglesIn two

UWDE

VWFEUVDF

DFE UVW

by ____SSS

Not congruent.Not enough Information to Tell

R

TS

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