Question

Suppose angle CBA is congruent to angle DEA. Using only the information provided in this problem, can you use the SSS Postulate or the SAS Postulate to prove triangle ABC congruent to triangle AED?

both apply

by SAS only

neither apply

by SSS only

Answer 1

SAS only

Explanation:

Answer 2

Δ ABC congruent to Δ AED by SAS only

Explanation:

* Lets revise the cases of congruence

- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

and one side in the 2ndΔ

* Lets solve the problem

- In the two triangles ABC and AED

∵ m∠BAC = m∠EAD ⇒ given from the figure

∵ m∠CBA = m∠DEA ⇒ given

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠ACB = m∠ADE

- In Δ ABC and Δ AED

∵ AC = AD

∵ BC = ED

∵ m∠ACB = m∠ADE ⇒ including angle between the two sides

∴ Δ ABC ≅ Δ AED by SAS

- We can't prove from the given that AB = AE

* Δ ABC congruent to Δ AED by SAS only