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Using Congruent Triangles. Chapter 4. Objective. List corresponding parts. Prove triangles congruent (ASA, SAS, AAS, SSS, HL) Prove corresponding parts congruent (CPCTC) Examine overlapping triangles. Key Vocabulary - Review. Reflexive Property Vertical Angles Congruent Triangles

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objective
Objective
  • List corresponding parts.
  • Prove triangles congruent (ASA, SAS, AAS, SSS, HL)
  • Prove corresponding parts congruent (CPCTC)
  • Examine overlapping triangles.
key vocabulary review
Key Vocabulary - Review
  • Reflexive Property
  • Vertical Angles
  • Congruent Triangles
  • Corresponding Parts
review congruence shortcuts
Review: Congruence Shortcuts

**Right triangles only: hypotenuse-leg (HL)

congruent triangles cpctc
Congruent Triangles (CPCTC)

Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent.

  • Corresponding sides are congruent
  • Corresponding angles are congruent
slide7

Name the Congruence Shortcut or CBD

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

CBD

slide11

Example

AC

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

B 

For SAS:

A

For AAS:

slide12

Your Turn:

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

For AAS:

using congruent triangles cpctc
Using Congruent Triangles: CPCTC
  • If you know that two triangles are congruent, then you can use CPCTC to prove the corresponding parts in whose triangles are congruent.

*You must prove that the triangles are congruent before you can use CPCTC*

slide14

Example 1

In the diagram, AB and CD bisect each other at M. Prove that A B.

Use Corresponding Parts

slide15

Example 1

Statements

Reasons

1.

AB and CD bisect each other at M.

2.

2.

3.

3.

4.

4.

5.

5.

6.

6.

Use Corresponding Parts

1.

Given

the proof game
The Proof Game!

Here’s your chance to play the game that is quickly becoming a favorite among America’s teenagers: The Proof Game!

slide17

Rules:

Guys vs. Gals

Teams must take turns filling in the statements and reasons in the proofs to come.

If the statement/reason combo is correct, team gets 1 point. Next team continues.

If the statement/reason combo is incorrect, team loses 1 point. Next team fixes mistake.

Teammates cannot help the person at the board…he/she is on their own. Cheating loses all points!!

number one
Number One

Given: ∠ABD = ∠CBD, ∠ADB = ∠CDB

Prove: AB = CB

B

A

C

Statement

Reason

D

number two
Number Two

Given: MO = RE, ME = RO

Prove: ∠M = ∠R

O

R

Statement

Reason

M

E

number three
Number Three

Given: SP = OP, ∠SPT = ∠OPT

Prove:∠S = ∠O

O

T

S

Statement

Reason

P

number four
Number Four

Given: KN = LN, PN = MN

Prove: KP = LM

K

L

N

Statement

Reason

M

P

number five
Number Five

Given:∠C = ∠R, TY = PY

Prove: CT = RP

C

R

Y

Statement

Reason

P

T

number six
Number Six

Given: AT = RM, AT || RM

Prove:∠AMT = ∠RTM

A

T

Statement

Reason

M

R

slide24

Example 2

Sketch the overlapping triangles separately. Mark all congruent angles and sides. Then tell what theorem or postulate you can use to show∆JGH  ∆KHG.

SOLUTION

1.

Sketch the triangles separately and mark any given information. Think of ∆JGHmoving to the left and ∆KHGmoving to the right.

MarkGJH HKG andJHG KGH.

Visualize Overlapping Triangles

slide25

Example 2

2.

Look at the original diagram for shared sides, shared angles, or any other information you can conclude.

Add congruence marks to GHin each triangle.

3.

You can use the AAS Congruence Theorem to show that ∆JGH ∆KHG.

Visualize Overlapping Triangles

In the original diagram, GH and HG are the same side, so GHHG.

slide26

Example 3

Write a proof that shows ABDE.

ABC DEC

CB CE

AB DE

Use Overlapping Triangles

SOLUTION

slide27

Your Turn:

Redraw the triangles separately and label all congruences. Explain how to show that the triangles or corresponding parts are congruent.

GivenKJ KLandJ L,showNJML.

Use Overlapping Triangles

slide28

Your Turn:

3.

Given SPR QRPand Q S, show ∆PQR  ∆RSP.

Use Overlapping Triangles

joke time
Joke Time
  • What happened to the man who lost the whole left side of his body?
  • He is all right now.
  • What did one eye say to the other eye?
  • Between you and me something smells.
upcoming schedule
Upcoming Schedule
  • Quiz on Friday…HL, proofs, CPCTC, Isosceles Triangle Thm, overlapping triangles
  • Monday – vocabulary terms
  • Tues – Practice Day
  • Wednesday – Chapter 4 Test
  • **reminder – projects due Oct. 27!!!
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