ccgps analytic geometry (8-19-13)

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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

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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. - PowerPoint PPT Presentation

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Page 1: 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

Page 2: CCGPS Analytic Geometry (8-19-13)

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.

Page 3: CCGPS Analytic Geometry (8-19-13)

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

Page 4: CCGPS Analytic Geometry (8-19-13)

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.

Page 5: CCGPS Analytic Geometry (8-19-13)

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.

Page 6: CCGPS Analytic Geometry (8-19-13)

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

Corresponding Parts of Congruent Triangles are

Congruent

Page 7: CCGPS Analytic Geometry (8-19-13)

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

Page 8: CCGPS Analytic Geometry (8-19-13)

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

Page 9: CCGPS Analytic Geometry (8-19-13)

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

Page 10: CCGPS Analytic Geometry (8-19-13)

Overlapping sides are congruent in

each triangle by the REFLEXIVE property

Vertical Angles

are congruen

t

Alt Int Angles are congruent

given parallel

lines

Page 11: CCGPS Analytic Geometry (8-19-13)

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

A B

C

X Z

Y

INCLUDED ANGLE

Page 12: CCGPS Analytic Geometry (8-19-13)

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

Page 13: CCGPS Analytic Geometry (8-19-13)

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

Page 14: CCGPS Analytic Geometry (8-19-13)

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

Page 15: CCGPS Analytic Geometry (8-19-13)

Ex 2

statement. congruence a Write.

and , , trianglesIn two

UWDE

VWFEUVDF

DFE UVW

by ____SSS

Page 16: CCGPS Analytic Geometry (8-19-13)

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

Page 17: CCGPS Analytic Geometry (8-19-13)

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

Page 18: CCGPS Analytic Geometry (8-19-13)

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

Page 19: CCGPS Analytic Geometry (8-19-13)

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