cpctc - Ms. Huls` Math

Welcome Proof Experts!
 Pick up notes and take out your homework
 Take out your Transformation Test Corrections ( if you didn’t turn it in
last week)
Tonight’s HW:
1. P 262 #1-4, 7-11
2. Study guide # 1-8 ( skip 6, 7)
3. Make notecards from U2L10 and U2L11 (definition one side
and vocab. word on the other side
• Unit 2 Test is on Thursday/Friday
Agenda
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Review HW
4.6: CPCTC
Notecard Practice!
Begin 4.8: Isosceles and Equilateral Triangles
Review HW
On document camera
4-6 Triangle Congruence: CPCTC
Learning Objective:
• Use CPCTC to prove parts of triangles are congruent.
CPCTC (Corresponding Parts of Congruent Triangles
are Congruent)
• It is used to prove the remaining pieces of a triangle
are congruent after you have proved that two
triangles are congruent.
– Similar to when we used ______________ to prove that
two lines are ________________.
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. ( write small!)
Lets first prove that the two
triangles are congruent. Use
a 2- column proof.
Whiteboards
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
Fill in the blanks
Example 2
Write this proof in two different ways.
Given: PR bisects QPS and QRS.
Prove: PQ  PS
Example 2 Continued
PR bisects QPS
and QRS
Given
RP  PR
Reflex. Prop. of 
∆PQR  ∆PSR
ASA
PQ  PS
CPCTC
QRP  SRP
QPR  SPR
Def. of  bisector
Example 3
Given: J is the midpoint of KM and NL.
Prove: KL || MN
Example 3 Continued
Statements
Reasons
1. J is the midpoint of KM and NL.
1. Given
2. KJ  MJ, NJ  LJ
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. KL || MN
6. Conv. Of Alt. Int. s Thm.
Whiteboards
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! ( CPCTC)
King/Queens’ Court
• I don’t want to stand up here all period and do
proofs so we are going to play a game!
• You are competing against everyone in the
classroom to be the first to finish.
• If you finish you will come to the front board and
compete against all of the students in the class.
King/Queens’ Court
• I am going to post a question on the board.
• When you finish, raise your board.
– If you are right, you become the king/queen.
– If you are wrong you must wait for two other students
to raise their board before you can raise yours again.
King/Queens’ Court
• QUESTIONS?!?
ROUND 1
ROUND 2
Find the measure of the question mark.
ROUND 3
ROUND 4
Find the measure of the question mark.
ROUND 5
Notecard Practice