Answer:
Yes, by AAS ⇒ 2nd answer
Step-by-step explanation:
* <em>Lets revise the cases of congruence</em>
- <u><em>SSS</em></u> ⇒ 3 sides in the 1st Δ ≅ 3 corresponding sides in the 2nd Δ
- <u><em>SAS</em></u> ⇒ 2 sides and including angle in the 1st Δ ≅ 2 corresponding
sides and including angle in the 2nd Δ
- <u><em>ASA</em></u> ⇒ 2 angles and the side whose joining them in the 1st Δ ≅
2 corresponding angles and the side whose joining them in the 2nd Δ
- <em><u>AAS</u></em> ⇒ 2 angles and one side in the first triangle ≅ 2 corresponding
angles and one side in the 2ndΔ
* <em>Lets solve the problem</em>
- In 2 Δs ADC and EBC
∵ <em>∠ACE is a common angle</em> in the two triangles ⇒ given
∵ <em>∠CAD ≅ ∠CEB</em> ⇒ because they marked with the same symbol
∵ <em>DC ≅ BC</em> ⇒ because they marked with the same symbol
- Two angles and one side in Δ ADC ≅ two corresponding angles
and one side in Δ EBC
∴ <u><em>Triangles ADC and EBC congruent by AAS</em></u>
* Yes Triangles ADC and EBC congruent by AAS
