Triangles (SSS,SAS,ASA)

Geometric Proofs

What is known?

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

•  $\overline{BD}\$  bisects  $\angle ABC$  

•  $\Delta ABD\ \cong\ \Delta CBD$  

How do we know that  $\Delta ABD\ \cong\ \Delta CBD$  

•  $\overline{AB}\ \cong\ \overline{CB}$  and  $\overline{BD}$  bisects  $\angle ABC$  are GIVEN

•  $\angle ABD\ \cong\ \angle CBD$   : For what reason?

• Reflexive property next, what sides?

Multiple Choice

By what theorem are the two triangles congruent?

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

• Angle-Angle-Angle

• Side-Side-Angle

What is known?

• Q is the midpoint of  $\overline{SN}$  

•  $\angle1\ \cong\ \angle2$  

•  $\Delta SQR\ \cong\ \Delta NQM$  

How do we know that  $\Delta SQR\ \cong\ \Delta NQM$  

• Q is the midpoint of  $\overline{SN}$  and  $\angle1\ \cong\ \angle2$  are GIVEN

•  $\overline{SQ}\ \cong\ \overline{NQ}$  ... 

Multiple Choice

Knowing that Q is the midpoint of  $\overline{SN}$  . How do we know that  $\overline{SQ}\ \cong\ \overline{NQ}$  ?

• Definition of a midpoint

• Definition of a perpendicular bisector

• Definition of an angle bisector

• Reflexive property

Multiple Choice

For what reason are  $\angle MQN\ \cong\ \angle RQS$  

• Vertical Angles

• Corresponding Angles

• Alternate Interior Angles

• Angle-Angle-Angle

Multiple Choice

By what theorem are triangles  $\Delta MNQ\ \ and\ \ \Delta RSQ$  congruent?

• Side-Angle-Side

• Angle-Side-Angle

• Angle-Angle-Side

• Side-Side-Angle

• Side-Side-Side

Multiple Select

Recap: What are the theorems for congruence in triangles?

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

• Side-Side-Angle

• Angle-Angle-Angle

Multiple Choice

What theorem makes $\Delta ABC\ \cong\ \Delta DEF$ ?

• Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

• Side-Side-Angle

Multiple Choice

What theorem makes  $\Delta ABC\ \cong\ \Delta DEF$  ?

• Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

• Hypotenuse-Leg

Multiple Choice

What theorem makes $\Delta ABC\ \cong\ \Delta DEF$ ?

• Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

• Side-Side-Angle