Question

Using only the markings in the diagram, what theorem can be used to prove that the triangles are congruent?

A) AAA

B) AAS

C) SAS

D) SSS

Answer 1

Answer: B) AAS

Explanation:

From the given picture of triangles.

In ΔABC and ΔDEF , we have

`\angle{A}\cong\angle{D}`

`\angle{C}\cong\angle{F}`

`\overline{BC}\cong\overlien{EF}`

So by AAS theorem , we have

ΔABC ≅ ΔDEF

Hence, AAS theorem can be used to prove that the triangles are congruent.

• AAS theorem says that if two angles and any side of one triangle are congruent to two angles and any side of other triangle then we say that the triangles are congruent.

Answer 2

Triangles are congruent by AAS theorem ⇒ answer B

Explanation:

* Lets solve the problem

- The given:

- In the two Δs ACB and DFE

∵ m∠BAC = m∠EDF ⇒ pair of congruent angles

∵ m∠BCA = m∠EFD ⇒ pair of congruent angles

∵ BC = EF ⇒ pair of congruent sides

- The two triangles have two pairs of congruent corresponding angles

- The two triangles have one pair of congruent corresponding sides

∴ Δ ACB ≅ Δ DFE

∴ The two triangles are congruent by AAS theorem

* Triangles are congruent by AAS theorem