triangles abc and def have the following characteristics:
∠b and ∠e are right angles
∠a ≅ ∠d
bc ≅ ef
which congruence theorem can be used to prove △abc ≅ △def?
asa
hl
aas
sas

Question

Accepted Answer

# Brief Explanations:
- **AAS (Angle - Angle - Side)**:
    - We know that $\angle B=\angle E = 90^{\circ}$ (right angles), $\angle A=\angle D$ (given), and $BC = EF$ (given).
    - In the AAS congruence theorem, if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, then the two triangles are congruent. Here, the non - included side with respect to the two given angles ($\angle A$ and $\angle B$ in $\triangle ABC$, $\angle D$ and $\angle E$ in $\triangle DEF$) is $BC$ (in $\triangle ABC$) and $EF$ (in $\triangle DEF$) and they are equal.
- **Why not other theorems**:
    - **ASA (Angle - Side - Angle)**: For ASA, the side should be included between the two angles. Here, if we consider the angles $\angle A$ and $\angle B$ in $\triangle ABC$ (and $\angle D$ and $\angle E$ in $\triangle DEF$), the side $BC$ ($EF$) is not included between $\angle A$ and $\angle B$ ($\angle D$ and $\angle E$).
    - **HL (Hypotenuse - Leg)**: For HL, we need to know about the hypotenuse and a leg of right - angled triangles. We are not given any information about the hypotenuse of these right - angled triangles ($AC$ and $DF$).
    - **SAS (Side - Angle - Side)**: For SAS, we need two sides and the included angle. We are only given one side ($BC = EF$) and two angles ($\angle A=\angle D$ and $\angle B=\angle E$).

# Answer:
C. AAS

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: