Proving Triangle Congruence

The statement “two triangles are congruent if their corresponding sides and angles are congruent” is based on _________.

• Definition

• Postulate

• Theorem

• Axiom

In the figure  $\Delta POG\ \cong\ \Delta SOR$ , what is the side corresponding to  $\overline{PO}$  ?

•  $\overline{SO}$  

•  $\overline{RD}$  

•  $\overline{RS}$  

•  $\overline{OS}$  

In the figure  $\Delta DOS$  , what side is included between  $\angle D$   and  $\angle O$ ?

•  $\overline{DO}$  

•  $\overline{DS}$  

•  $\overline{SD}$  

•  $\overline{OS}$  

Jancent knows that  $\overline{AB}\ \cong\ \overline{XY}$  and  $\overline{AC}\ \cong\ \overline{XZ}$ . What other information must he know to prove that  $\Delta ABC\ \cong\ \Delta XYZ$  by SAS congruence postulate?

•  $\angle B\ \cong\ \angle Y$  

•  $\angle C\ \cong\ \angle Z$  

•  $\angle A\ \cong\ \angle X$  

•  $\angle A\ \cong\ \angle B$  

Miguel knows that in$\Delta MIG\$ and  $\Delta JAN$ ,  $\overline{MI}\ \cong\ \overline{JA}\ ,\ \overline{IG}\ \cong\ \overline{AN}\$ and  $\overline{MG}\ \cong\ \overline{JN}$ . Which congruence postulate can he use to prove that  $\Delta MIG\ \cong\ \Delta JAN$ ?

• ASA

• SAS

• AAA

• SSS

Why is it important to have a basis for reasoning in writing proofs when proving the congruence of triangles?