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CPCTC

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L

_____ _____

J

N

K

M

Be able to use CPCTC to find unknowns in congruent triangles!

Quick Review

Are these triangles congruent? By which postulate/theorem?

Oh, and what is the Reflexive Property again?

It says something is equal to itself. EX: A A or AB AB.

C.P.C.T.C.

Corresponding Parts of Congruent Triangles are CONGRUENT!!

Once you have shown triangles are congruent, then you can make some CONCLUSIONS about all of the corresponding parts (_______ and __________) of those triangles!

sides

angles

B

Y

Z

C

X

A

Are the triangles congruent? By which postulate or theorem?

Yes; ASA

What other parts of the triangles are congruent by CPCTC?

If B = 3x and Y = 5x –9, find x.

BY

3x = 5x - 9

9 = 2x

AB ZY

BC YX

C

L

3

4

1

2

R

S

1.1. ___________

3. 3. ___________

PROOFS!

Given:

Prove:

Given

2. _______________2. Reflexive

SAS

CPCTC

4. _______________4. ___________

C

V

Given:

R

H

A

E

Prove:

1. _____________________1. Given

2. _____________________2. SSS

CPCTC

3. _____________________3. ________

R

C

Q

Y

P

T

State why the two triangles are congruent and write the congruence statement. Also list the other pairs of parts that are congruent by CPCTC.

YQ

CT RP

CY RP

AAS

40 yd

30 yd

24.5 yd

30 yd

40 yd

A geometry class is trying to find the distance across a small lake. The distances they measured are shown in the diagram. Explain how to use their measurements to find the distance across the lake.

Vertical angles are congruent.

The triangles are congruent by SAS.

The width of the lake has to be 24.5 yd by CPCTC.

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

- One angle pair is congruent, because they are vertical angles.

- Two pairs of sides are congruent, because their lengths are equal.
- Therefore the two triangles are congruent by SAS.
- By CPCTC, the third side pair is congruent, so JK = 41 ft.

1. N P; NO || MP

Given: NO || MP, N P

Prove: MN || OP

3. MO MO

6. MN || OP

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.

6. DX BX

Given: X is the midpoint of AC . 1 2

Prove: X is the midpoint of BD.

Statements

Reasons

1. X is mdpt. of AC. 1 2

1. Given

2. AX = CX

2. Def. of mdpt.

3. AX CX

3. Def of

4. AXD CXB

4. Vert. s Thm.

5. ∆AXD ∆CXB

5. ASA Steps 1, 4, 5

6. CPCTC

7. Def. of

7. DX = BX

8. X is mdpt. of BD.

8. Def. of mdpt.