Statements	Reasons
$$\overline{CB}\cong\overline{ZY}$CB≅ZY$	Given
$$\overline{AC}\cong\overline{XZ}$AC≅XZ$	Given
$$\overline{AB}\cong\overline{XY}$AB≅XY$	Given
$$\Delta ABC\cong\Delta XYZ$ΔABC≅ΔXYZ$	$$\left[\text{____}\right]$[____]$

Select the correct reason to complete the proof.

$Side-angle-side congruence (SAS)$

$Angle-angle-side congruence (AAS)$

Side-side-angle congruence (SSA)

$Side-side-side congruence (SSS)$

$Angle-side-angle congruence (ASA)$

Medium

< 1min

This two-column proof shows that $$\Delta PQR\cong\Delta RSP$ΔPQR≅ΔRSP$ in the attached diagram, but it is incomplete.

Medium

< 1min

This two-column proof shows that $$\Delta DEH\cong\Delta FEG$ΔDEH≅ΔFEG$ in the attached diagram, but it is incomplete.

Medium

< 1min

Consider the following diagram:

Hard

1min

Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.

Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.

Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.

Construct proofs, including proofs by contradiction.

Judge the validity of arguments and give counterexamples to disprove statements.

4.02 SAS and SSS congruence criteria

Interactive practice questions