Question

Given: start overline, b, e, end overlinebe bisects angle, d, b, c∠dbc and start overline, b, e, end overline, \parallel, start overline, a, c, end overline, .be∥ac. prove: start overline, a, b, end overline, \cong, start overline, b, c, end overlineab≅bc.

Answer 1

To prove that triangles ABC and CBA are congruent, we can use the transitive property of parallel lines to show that they share a common side. Similarly, we can prove that they have a common angle. Therefore, by the Side-Angle-Side (SAS) congruence postulate, we can conclude that ABC and CBA are congruent triangles, resulting in AB ≅ BC.

Step-by-step explanation:

To prove that τABC and τCBA share a common side, we can use the transitive property of parallel lines. Since τCBE and τABC share a common side, and τCBE and τ2019CBA share a common side, then τABC and τCBA also share a common side.

Similarly, we can prove that τABC and τCBA have a common angle. Since τCBE and τABC have a common angle at B, and τCBE and τ2019CBA have a common angle at B, then τABC and τCBA also have a common angle at B.

Therefore, by the Side-Angle-Side (SAS) congruence postulate, we can conclude that τABC and τCBA are congruent triangles, and thus the sides AB and BC are congruent, as stated in the given statement.