S6 Triangles Topic 6

We are given that  $\overline{AB}\cong\overline{BC};$  therefore,  $\angle A\cong\angle C$  by the

• Base Angles Theorem
  

• Congruent Angles Theorem
  

• Alternate Exterior Angles Theorem
  

• Alternate Interior Angles Theorem
  

Tags

CCSS.HSG.SRT.B.5

Because of the Definition of a Midpoint, we know that

• $\overline{AE}\cong\overline{BE}$

• $\overline{AE}\cong\overline{CE}$

• $\overline{AE}\cong\overline{BC}$

• $\overline{AE}\cong\overline{AE}$

Tags

CCSS.HSG.SRT.B.5

 We can conclude that  $\Delta ABE\cong\Delta CBE$  by

• SSS

• AA

• SAS

• ASA

Tags

CCSS.HSG.SRT.B.5

We can conclude that  $\angle ABE\cong\angle CBE$  by

• Definition of Angle Bisector
  

• Reflexive Property
  

• CPCTC

• Angle Addition Postulate
  

Tags

CCSS.HSG.SRT.B.5

We are given that  $\overline{WZ}\parallel\overline{XY},\ \overline{WX}\parallel\overline{ZY};$  therefore __________________ by Reflexive Property of Congruence.

•  $\overline{WZ}\cong\overline{WZ}$  

•  $\overline{XZ}\cong\overline{XZ}$  

•  $\overline{XY}\cong\overline{XY}$  

•  $\overline{WX}\cong\overline{WX}$  

Tags

CCSS.HSG.CO.C.11

We know that  $\angle WZX\cong\angle YXZ$  because

• Definition of a Parallelogram
  

• Alternate Interior Angles Theorem
  

• Corresponding Angles Postulate
  

• AA

Tags

CCSS.HSG.CO.C.11

We can conclude that  $\Delta ZWX\cong\Delta XYZ$  by

• SSS

• ASA

• AAS

• SAS

Tags

CCSS.HSG.SRT.B.5

We can conclude that  $\overline{WZ}\cong\overline{XY}$  by 

• Reflexive Property
  

• CPCTC

• Definition of Parallelogram
  

• AA

Tags

CCSS.HSG.CO.C.11

Bayleigh argued that, in the diagram,  $\angle ONP\cong\angle QPN$  because of SSS and CPCTC. Which statement is true?

• Bayleigh's argument is correct.
  

• Bayleigh should have used a reason other than CPCTC to make her final conclusion.
  

• Bayleigh does not have enough information to prove the triangles congruent by SSS.
  

• Bayleigh should have used SAS, not SSS to prove the triangles are congruent.
  

Tags

CCSS.HSG.SRT.B.5