Question

What postulate or theorem can be used to prove that these two triangles are congruent?

Answer 1

Answer:

AAS postulate can be used to prove that these two triangles are congruent

Step-by-step 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

∵ There is a pair of vertically opposite angles

∵ The vertically opposite angles are congruent ⇒ (1)

∵ There are two angles have the same mark

∴ These marked angles are congruent ⇒ (2)

∵ There are two sides have the same mark

∴ These two marked sides are congruent ⇒ (3)

→ From (1), (2), and (3)

∴ The two triangles have 2 angles and 1 side congruent

→ By using case 4 above

∴ The two triangles are congruent by the AAS postulate of congruency.

AAS postulate can be used to prove that these two triangles are congruent