Do the triangles have a side in common? Use the definition of congruent polygons.
Statements
Reasons
1.
BA≅DC and ∠BAC ≅ ∠DCA
1.
Given
2.
AC = CA
2.
Reflexive Property of Congruent Segments
3.
△ ABC ≅ △ CDA
3.
Side-Angle-Side (SAS) Congruence Postulate
4.
BC≅DA
4.
Definition of Congruent Polygons
Practice makes perfect
In the given diagram let's highlight the side AC, which is common for both â–³ ABC and â–³ CDA.
By the Reflexive Property of Congruent Segments we get AC ≅ CA. Let's write all the congruent parts we have.
cc
AB ≅ CD & Side
∠BAC ≅ ∠DCA & Included Angle
AC ≅ CA & Side
By applying the Side-Angle-Side (SAS) Congruence Postulate we get △ ABC ≅ △ CDA, which implies that BC ≅ DA. Finally, we write the two-column proof table.
