CPCTCCPCTC

MNKΔLJK

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

Are these triangles congruent? By which postulate/theorem?

_____ _____J

L

K N

M

Oh, and what is the Reflexive Property again?

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

Once you have shown triangles are congruent, then you can make some CONCLUSIONS about all of the

corresponding parts (_______ and __________) of those triangles!

Corresponding Parts of Congruent Triangles are CONGRUENT!!

C.P.C.T.C.

sides angles

CPCTCCPCTC

Are the triangles congruent? By which postulate or theorem?

What other parts of the triangles are congruent by CPCTC?

A

B

C

X

Y

Z

If B = 3x and Y = 5x –9, find x.

Yes; ASA

B Y

BC YX

AB ZY

3x = 5x - 9

9 = 2x

x2

9

2. _______________ 2. ReflexiveCSCS

43

Given:

SRSL21

Prove: 3 4

4. _______________ 4. ___________

L

SR

C

1 2

3 4

Given

SAS

CPCTC

C

A

R

V

E

H

Given:

VECAEHAR HVRC

Prove: HR

1. _____________________ 1. Given

2. _____________________ 2. SSS

3. _____________________ 3. ________

VECA;EHAR ;HVRC

VHECRA

HR CPCTC

State why the two triangles are congruent and write the congruence statement. Also list the

other pairs of parts that are congruent by CPCTC.

C

T

Y

R

P

Q

AASAAS

Y Q

CY RP

CT RP

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.

30 yd

30 yd

40 yd24.5 yd

40 yd

The triangles are congruent by SAS.

Vertical angles are congruent.

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?

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.

5. CPCTC5. NMO POM

6. Conv. Of Alt. Int. s Thm.

4. AAS4. ∆MNO ∆OPM

3. Reflex. Prop. of

2. Alt. Int. s Thm.2. NOM PMO

1. Given

ReasonsStatements

3. MO MO

6. MN || OP

1. N P; NO || MP

Prove: MN || OP

Given: NO || MP, N P

6. CPCTC

7. Def. of 7. DX = BX

5. ASA Steps 1, 4, 55. ∆AXD ∆CXB

8. Def. of mdpt.8. X is mdpt. of BD.

4. Vert. s Thm.4. AXD CXB

3. Def of 3. AX CX

2. Def. of mdpt.2. AX = CX

1. Given1. X is mdpt. of AC. 1 2

ReasonsStatements

6. DX BX

Given: X is the midpoint of AC . 1 2Prove: X is the midpoint of BD.