CPCTC in Proofs

Presentation

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Mathematics

•

10th Grade

•

Medium

•

CCSS

HSG.SRT.B.5, HSG.CO.B.7, 8.G.A.2

Standards-aligned

Erin Inman

Used 160+ times

FREE Resource

6 Slides • 16 Questions

You should be familiar that if two triangles are congruent, then all their corresponding parts are congruent as well.

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

Multiple Choice

What does CPCTC stand for?

Congruent parts of congruent triangles are congruent

Corresponding parts of congruent triangles are congruent

Corresponding parts of corresponding triangles are corresponding

Corresponding parts of congruent triangles are Canadian.

Multiple Choice

Remember order matters. Which of the following is true?

∆FGH ≅ ∆VHW

∆HFG ≅ ∆HWV

∆HGF ≅ ∆VHW

∆FGH ≅ ∆VWH

Multiple Choice

If ∆LMK ≅ ∆LMT, then
∠K ≅ ____

∠T

∠M

∠L

Multiple Choice

∆ABC≅∆XYZ
which is true?

AB≅XY

AB≅YX

AB≅XZ

BC≅CB

Multiple Choice

What is the correct congruence statement? ΔDEC ≅________

ΔAEB

ΔEAB

ΔBEA

Not Congruent

To prove CPCTC:

First, we need to prove that the two triangles are congruent with the help of any one of the triangle congruence criteria.

In the figure, determine how you could prove the triangles congruent.

SSS, SAS, AAS, ASA, HL

Multiple Choice

What reason could prove the triangles congruent?

SSS

SAS

AAS

ASA

Hopefully you recognize

BC≅CD
Vertical angles are congruent
AC≅EC

This is enough to prove the triangles congruent by SAS.

Since the triangles are congruent, all the corresponding parts of the triangles are congruent.

Multiple Choice

What congruency postulate proves the triangles congruency?

SAS

ASA

SSS

Multiple Choice

Are the triangles congruent, if yes, why?

SSS

ASA

Not Congruent

Multiple Choice

∆ABC≅∆XYZ

which is true?

AB≅XY

BC≅CB

AB≅YX

AB≅XZ

Multiple Select

After proving the triangles are congruent by HL Theorem, which statements are true for CPCTC?

$\angle X\cong\angle V$

$\angle U\cong\angle X$

$XW\cong VW$

$\angle XUW\cong\angle UWV$

Multiple Select

After proving the triangles are congruent by SAS postulate, which statements are true for CPCTC?

$\angle D\cong\angle A$

$\angle B\cong\angle D$

$DE\cong AE$

$EC\cong AB$

$BA\cong DC$

Multiple Choice

If ∆PIG ≅ ∆COW, WO≅?

Multiple Choice

If ΔDEF ≅ ΔRST, then we can conclude that DE = what?

When do I use CPCTC?

In a Geometric Proof.

If you are trying to prove two corresponding parts of a triangle are congruent, and they aren't a reflexive side, vertical angles, alternate interior angles, then CPCTC is the way to go.

In the figure shown,

PROVE: ∡A≅∡E

FIRST--prove the triangles congruent.

THEN once the triangles are congruent, all corresponding parts are ≅

CPCTC is the last REASON

Example:

In the figure shown,

PROVE: ∡A≅∡E

Before using CPCTC, show that the two triangles are congruent.

REMEMBER:

Multiple Choice

Determine the reasons for the remaining steps of the proof.

Definition of Isosceles Triangle; HL; CPCTC

Definition of Isosceles Triangle; SAS; CPCTC

Isosceles Triangle Theorem; HL; CPCTC

Isosceles Triangle Theorem; SAS; CPCTC

Multiple Choice

Determine the reasons for the remaining steps of the proof.

Definition of Midpoint; Converse of Isosceles Triangle Theorem; SAS; CPCTC

Definition of Midpoint; Isosceles Triangle Theorem; HL; CPCTC

Isosceles Triangle Theorem; Converse of Isosceles Triangle Theorem; HL; CPCTC

Isosceles Triangle Theorem; Converse of Isosceles Triangle Theorem; SAS; CPCTC

Multiple Choice

Determine the reasons for the remaining steps of the proof.

Alternate Interior Angles Theorem; Vertical Angles Theorem; AAS; CPCTC

Definition of Parallel Lines; Vertical Angles Theorem; AAS; CPCTC

Alternate Interior Angles Theorem; Reflexive Property; ASA; CPCTC

Definition of Parallel Lines; Reflexive Property; ASA; CPCTC

You should be familiar that if two triangles are congruent, then all their corresponding parts are congruent as well.

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

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