which statements are true about additional information for proving that the triangles are congruent? select…
which statements are true about additional information for proving that the triangles are congruent? select two options. if ∠a≅∠t, then the triangles would be congruent by asa. if ∠b≅∠p, then the triangles would be congruent by aas. if all the angles are acute, then the triangles would be congruent. if ∠c and ∠q are right angles, then triangles would be congruent. if (overline{bc}congoverline{pq}), then the triangles would be congruent by asa.
Answer
Explanation:
Step1: Recall congruence postulates
ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent.
Step2: Analyze each option
- For “If $\angle A\cong\angle T$, then the triangles would be congruent by ASA.”: We already have $\angle C\cong\angle Q$ (from the figure's marked angles). If $\angle A\cong\angle T$, and the included side between these angles is part of the given information in the triangles' setup, this satisfies ASA.
- For “If $\angle B\cong\angle P$, then the triangles would be congruent by AAS.”: Given $\angle C\cong\angle Q$, if $\angle B\cong\angle P$, then with the non - included side (the side opposite the given angles), this satisfies AAS.
- For “If all the angles are acute, then the triangles would be congruent.”: Just knowing angles are acute is not a congruence postulate.
- For “If $\angle C$ and $\angle Q$ are right angles, then triangles would be congruent.”: Knowing two angles are right angles is not sufficient for congruence without more side or angle information.
- For “If $\overline{BC}\cong\overline{PQ}$, then the triangles would be congruent by ASA.”: This does not satisfy ASA as the side is not the included side for the known congruent angles.
Answer:
If $\angle A\cong\angle T$, then the triangles would be congruent by ASA; If $\angle B\cong\angle P$, then the triangles would be congruent by AAS.