Question

Indicate the method you would use to prove the two A's . If no method applies, enter "none".

30
70*
10
10
360
70°
O SSS
OSAS
OASA
O AAS
None

Answer 1

The method would use to prove that the two Δs ≅ is AAS ⇒ D

Explanation:

Let us revise the cases of congruence:

1. SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
2. SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
3. 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
4. AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
5. HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ

In the given figure

∵ The two triangles have an angle of measure 30°

∵ The two triangles have an angle of measure 70°

∵ The two triangles have a side of length 10

∴ The two triangles have two equal angles and one equal side

→ By using rule 4 above

∴ The two triangles are congruent by the AAS rule

∴ The method would use to prove that the two Δs ≅ is AAS