Proving Triangle Congruence Using Postulates

Identify the missing statement or reason

• Reflexive Property

• Definition of Midpoint

• Given

• Vertical Angles Theorem

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

• Given

• Transitive Property

• Definition of Congruent Angles

• Vertical Angles are congruent.

Which of the following is a correct statement and reason for the proof shown?

What is the justification?

• Symmetric Prop.

• Angle addition postulate

• Reflexive Prop

• Transitive Prop.

Can the triangles be proven congruent?  If so, how?

• ASA

• AAS

• SAS

• Cannot be proven congruent

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Explain the difference between proving triangles congruent using the SAS and SSS Congruence Postulates.

• SAS requires two sides and the included angle, while SSS requires three sides.

• SAS requires three sides, while SSS requires two sides and the included angle.

• SAS requires two angles and the included side, while SSS requires three angles and the included side.

• SAS requires three sides and the right angle, while SSS requires three angles.

Use the given information to prove that triangles ABC and CDB are congruent. Explain your reasoning.

Triangles ABD and DCB are right triangles​ (a)   AB, BC CD and DA​ (b)   AB=AB​ (c)   . So, triangle ABD and CDB are congruent by ​ ​ (d)  

​​

​ ​

• because ABCD is a square

• are congruent because ABCD is a square

• because reflexive property

• HL

• AAA

• Opposite angles are congruent

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate.

• Yes by SAS

• No, because ZW is not congruent to ZW, ZX is not a perpendicular bisector.

• Cannot be determined

• Yes, because ZW is congruent to ZW, ZX is a perpendicular bisector., and WX=XY