Chapter Test
Sign In
If we look at the diagram, we see that ∠ACB and ∠ECD are vertical angles. According to the Vertical Angles Congruence Theorem, vertical angles are congruent.
Since we now know that two sides and the included angle of △ABC are congruent to two sides and the included angle of △EDC, we can claim by the SAS Congruence Theorem that the triangles are congruent.
Let's also show this as a two-column proof.
Statement | Reason |
CA≅CB≅CD≅CE | Given |
∠ACB≅∠ECD | Vertical Angles Congruence Theorem |
△ABC≅△EDC | SAS Congruence Theorem |