Triangle Congruence Theorems

Geom: CPCTC

G.CO.B.8 Guide 4

Multiple Select

$$\Delta TNJ\cong\Delta RPQ$$  Which of the followng are true based on the congruence statement? Select all that apply. 

• $$\angle T\cong\angle R$$  

• $$\overline{TR}\cong\overline{JQ}$$  

• $$\overline{TN}\cong\overline{RP}$$  

• $$\angle N\cong\angle J$$  

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

True or False: I can use CPCTC before I establish that the triangles are congruent.

• True

• False

Multiple Choice

Fill in the reason for number 3. 

• Reflexive property
• Symmetric Property
• Transitive property
• Substitution property

Multiple Choice

Find the measure of $$\angle NJZ$$  

• 38

• 90

• 52

• 128

Multiple Choice

What is the justification (reason)?

• reflexive property
• definition of segment bisect
• definition of a midpoint
• substitution property

Multiple Choice

Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?

• No
• Sometimes
• Yes
• N/A

Multiple Choice

If AB = BC and BC = CD, then CD = AB is an example of what?

• Reflexive Property
• Symmetric Property
• Transitive Property
• Transformative Property

Multiple Choice

What is the "reason" for step 3 of the proof?

• Vertical Angle Theorem
• given
• reflexive property
• proof

Multiple Choice

Fill in the blank.

• Given
• Reflexive Property
• Transitive Property
• They're the same side!!!!!! 

Multiple Choice

What postulate proves these triangles congruent?

• HL
• SSS
• SAS
• ASA

Multiple Choice

What does SAS stand for?

• Side-Angle-Side
• Super-Awesome-Side
• Side-Angle-Supersized
• Sensationally Awesome Superman

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS
• ASA
• AAA
• Not Congruent

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS
• SAS
• ASA
• Not Congruent

Multiple Choice

Are the triangles congruent, if yes, why?

• SAS
• ASA
• SSS
• Not Congruent

Multiple Choice

What is the correct congruence statement?  ΔDEC ≅________

• ΔAEB
• ΔEAB
• ΔBEA
• Not Congruent

Multiple Choice

All of the following prove triangles congruent except

• SSS
• SAS
• CPCTC
• HL

Multiple Choice

You should use CPCTC ______

• before you prove triangles congruent
• to prove two triangles congruent
• after proving triangles congruent to get the corresponding parts congruent
• never use CPCTC it is not a thing

Multiple Choice

Fill in the missing pieces of the proof.

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Reflexive Property, Vertical Angles Thm.
• Transitive Property, SSS(Side-Side-Side)

Multiple Choice

Which of the following is NOT a valid reason to prove congruent triangles?

• SSA
• ASA
• SAS
• SSS

Multiple Choice

Line HI and Line FC are______________.

• Parallel

• Skew

• Intersecting

Multiple Choice

Angle 2 is congruent to Angle _____ because when parallel lines are cut by a transversal, corresponding angles are congruent.

• 3

• 6

• 8

• 7

Multiple Choice

What type of lines are lines FE and GH?

• Parallel

• Skew

• Intersecting

Multiple Choice

True/False: a single rotation could map Triangle ABC onto Triangle A'B'C'.

• True

• False

Multiple Choice

If you were given that  $$\overline{BC}\cong\overline{DC},$$  what other information would you need to be given to prove the triangles congruent by SAS? 

• $$\angle BAC\cong\angle DAC$$  

• $$\angle BCA\cong\angle DCA$$  

• $$\angle B\cong\angle D$$  

• $$\overline{AD}\cong\overline{AB}$$  

Multiple Choice

What reason goes in the box for reason 2?

• Alternate Interior Angles

• Vertical Angles

• Reflexive Property

• CPCTC

Multiple Choice

What reason goes in the blank for reason 3?

• CPCTC

• ASA

• SAS

• SSS

Multiple Choice

What is the reason for statement 2?

• Vertical angles

• Reflexive Property

• Definition of Midpoint

• CPCTC

Multiple Choice

$$\angle B\cong\angle?$$  because of alternate interior angles

• A

• B

• C

• D

• E

Multiple Choice

What is the reason for statement 6?

• ASA

• SSS

• CPCTC

• Definition of Midpoint

• Reflexive Property