Basic Geometric Proofs

Geometric Proof

Properties for your notes

• Reflexive

• Vertical Angle Theorem

• Definition of a Bisector

• Definition of a Kite

• Definition of a Perpendicular

• Definition of a Rectangle

• Definition of a Square

And more properties

• SSS

• SAS

• ASA

• AAS

• HL

• IF any of the above are proven, you can use CPCTC to prove the rest of the triangle is true

Multiple Choice

What is the "statement" for step 2 of the proof?

• AD=AD
• AD=DA
• HD=DN
• HA = AN

Multiple Choice

Which is the correct reason for statement 2 in the proof?

• Given
• Transitive Property
• Definition of Congruent Angles
• Vertical Angles are congruent.

Multiple Choice

AB = AB

• Reflexive POE
• Transitive POE
• Symmetric POE
• Distributive POE

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

What is the "statement" for step 2 of the proof?

• AD=AD
• AD=DA
• HD=DN
• HA = AN

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS
• SAS
• AAS
• 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

• AAS

• Not congruent

Multiple Choice

Are the triangles congruent, if yes, why?

• SAS

• ASA

• AAS

• Not congruent

Multiple Choice

When using hypotenuse leg (HL) in a proof, you must first state ...

• CPCTC.
• there are right triangles.
• that vertical angles are congruent.
• the reflexive property.

Multiple Choice

State if the two triangles are congruent.  If they are, state how you know.

• A
• B
• C
• D

Multiple Choice

What is statement #6?

• BC≅BC
• BC≅DA
• ∠BCD≅BAC
• AB≅CD

Multiple Choice

What is reason #4?

• ASA
• SAS
• HL
• AAS

Multiple Choice

What is statement #3?

• FH≅FH
• GF≅GF
• IH≅IH
• GF≅FI

Multiple Choice

What is reason #2?

• Definition of Midpoint
• Definition of Perpendicular
• Definition of Bisect
• Definition of Right Triangle

Multiple Choice

What is reason #4?

• ASA
• SAS
• HL
• AAS

Multiple Choice

What is statement #4?

• ∆HFG≅∆IHF
• ∆FHG≅∆IHF
• ∆GFH≅∆IFH
• ∆HFG≅∆IFH

Multiple Choice

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

• HT=TA
• HA=AH
• MA=AM
• MA=MH

Multiple Choice

What are the 2 missing pieces of information?

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Transitive Property, SSS(Side-Side-Side)
• Reflexive Property, SSS(Side-Side-Side)

Multiple Choice

What is the "reason" for step 5 of the proof?

• Angle Bisector Theorem
• Reflexive property
• CPCTC Theorem
• Proof

Multiple Choice

Find x.  Assume that segments that appear to be   tangent are tangent.

• 2
• 11
• 7.6
• 9

Multiple Choice

Find the value of x.

• 31,3
• 8
• 16.3
• -8

Multiple Choice

find the measure of y

• 30
• 60
• 90
• 180

Multiple Choice

If DA bisects IE, then

• ID=ED
• IA=EA
• <IDA=<EDA
• <IAD and <EAD are right angles

Multiple Choice

What is Reason F?

• Given

• Definition of Congruence

• Triangle Congruence

• CPCTC

Multiple Choice

What is Reason B?

• Definition of Equality

• Definition of Congruence

• Definition of Bisector

• Definition of Midpoint

Multiple Choice

What is #4 Reason

• Definition of Midpoint

• Perpendicular Bisector

• Segment Bisector

• Reflexive Property

Multiple Choice

What is reason #2?

• Definition of Midpoint
• Definition of Perpendicular
• Definition of Bisect
• Definition of Right Triangle

Multiple Choice

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

• AD=DA
• AN = AH
• HD=ND
• HD=DN

Multiple Choice

Identify the  missing statement or reason

• Given
• Vertical Angles Theorem
• Definition of Angle Bisector
• Alternate Interior Angles Theorem

Multiple Choice

Which of these reflexive property statements is worth including because the shape is in both triangles?

• $$\overline{DA}\ \cong\ \overline{DA}$$

• $$\overline{BC}\ \cong\ \overline{BC}$$

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

• $$\overline{CA}\ \cong\ \overline{CA}$$