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Happy Wednesday!. Take out homework and notes from yesterday Take out your whiteboard and whiteboard marker Write down tonight’s homework in your homework log Tonight's Homework : Period 1: Pg . 262 #3, #10-11 & Quiz Corrections

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Happy Wednesday!

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Happy Wednesday!

  • Take out homework and notes from yesterday

  • Take out your whiteboard and whiteboard marker

  • Write down tonight’s homework in your homework log

    Tonight's Homework:

    Period 1: Pg. 262 #3, #10-11 & Quiz Corrections

    ALL PERIODS :p 246 #9, 13 p 256 #4 (Do them ALL as FLOW CHART PROOFS!) - this was the same homework assignment that you did on Monday night and get back today.

    , p 264 19-21


Do Now!

(1) Write a congruence statement for the triangles.


Whiteboards: Do Now

A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK?

First prove that the two triangles are congruent.

The two triangles are congruent by SAS.

By CPCTC, the third side pair is congruent, so JK = 41 ft.


Whiteboards

  • What does CPCTC stand for?

  • What do you need to prove first before you can use CPCTC?


4-6 Triangle Congruence: CPCTC

Learning Objective:

  • Use CPCTC to prove parts of triangles are congruent.


Example 1

Some hikers come to a river in the woods. They want to cross the river but decide to find out how wide it is first. So they set up congruent right triangles. The figure shows the river and the triangles. Find the width of the river, GH.


Example 2


Given:YW bisects XZ, XY ZY.

Z

Prove:XYW  ZYW

Lets try writing the two column proof as a flow chart!Start at the end at work backwards.

Example 3


ZW

WY

Example 3Continued


Given:PR bisects QPS and QRS.

Prove:PQ  PS

Example 4

Write using flow chart proof. If you need to, first do a 2-column proof, then a flow chart proof.


QRP SRP

QPR  SPR

PR bisects QPS

and QRS

RP PR

Reflex. Prop. of 

Def. of  bisector

Given

∆PQR  ∆PSR

ASA

PQPS

CPCTC

Example 4Continued


Given:NO || MP, N P

Prove:MN || OP

Example 5: Using CPCTC in a Proof


1. N  P; NO || MP

3.MO  MO

6.MN || OP

Example 5 Continued

Statements

Reasons

1. Given

2. NOM  PMO

2. Alt. Int. s Thm.

3. Reflex. Prop. of 

4. ∆MNO  ∆OPM

4. AAS

5. NMO  POM

5. CPCTC

6. Conv. Of Alt. Int. s Thm.


Given:J is the midpoint of KM and NL.

Prove:KL || MN

Whiteboards


1.J is the midpoint of KM and NL.

2.KJ  MJ, NJ  LJ

6.KL || MN

Whiteboards Continued

Statements

Reasons

1. Given

2. Def. of mdpt.

3. KJL  MJN

3. Vert. s Thm.

4. ∆KJL  ∆MJN

4. SAS Steps 2, 3

5. LKJ  NMJ

5. CPCTC

6. Conv. Of Alt. Int. s Thm.


Math Joke of the Day!

  • What do you write as the reason when using corresponding parts of congruent triangles in a proof?

  • See Peas Eat Easy!


More Flow Chart Proofs


Write a Flow Chart Proof

.

Given:X  V, YZW  YWZ, XY  VY

Prove: XYZ  VYW


Exit Ticket

  • Clear your desks.

  • You are going to write a proof using two methods ( paragraph, two-column, or flow chart)

  • Which way do you prefer and why?


Exit Ticket:

.

Given:JL bisects KLM, K  M

Prove:JKL  JML


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