Question
Example: What else is needed?
Consider the following diagram. What additional piece of information would you need to be able to state that â–³ABCDEF by the AAS Congruence Theorem?
B
D
C
F
= MULTIPLE-CHOICE QUESTION
What else is needed to use AAS? (there may be more than one option)
BC is congruent to EF
A
AB is congruent to DE
E
AC is congruent to DF
Consider the following diagram. What additional piece of information would you need to be able to state that â–³ABCDEF by the AAS Congruence Theorem?
B
D
C
F
= MULTIPLE-CHOICE QUESTION
What else is needed to use AAS? (there may be more than one option)
BC is congruent to EF
A
AB is congruent to DE
E
AC is congruent to DF
Answers
Answered by
GPT-4o mini
To determine what additional information is needed to state that triangle \( \triangle ABC \) is congruent to triangle \( \triangle DEF \) by the Angle-Angle-Side (AAS) Congruence Theorem, we need one angle from each triangle and the length of the side that is between them.
Given the options:
- **BC is congruent to EF**
- **AB is congruent to DE**
- **AC is congruent to DF**
The correct pieces of information that are required to apply the AAS theorem would be:
- One angle in triangle \( ABC \) (let's say \( \angle ABC \)) must be congruent to the corresponding angle in triangle \( DEF \) (let's say \( \angle DEF \)).
- The side opposite to those angles, such as \( AC \) congruent to \( DF \).
Depending on the specific angles in triangles \( ABC \) and \( DEF \) that are already known, the congruent side needed would properly align.
Therefore, at least one option needed to use AAS is **AC is congruent to DF**.
To finalize:
1. If you already have two angles known in both triangles, selecting **AB is congruent to DE** can also be used depending on which angles you know, but direct references to corresponding angles help clarify congruence.
So the option:
- **AB is congruent to DE** (if it connects with one known angle) or
- **AC is congruent to DF** (best fits in aligning with the mentioned angles)
Thus, you would need either **AC is congruent to DF** or **one corresponding angle congruence** which is not mentioned in your list. It's essential to confirm with the specific angles to draw a definitive conclusion.
Given the options:
- **BC is congruent to EF**
- **AB is congruent to DE**
- **AC is congruent to DF**
The correct pieces of information that are required to apply the AAS theorem would be:
- One angle in triangle \( ABC \) (let's say \( \angle ABC \)) must be congruent to the corresponding angle in triangle \( DEF \) (let's say \( \angle DEF \)).
- The side opposite to those angles, such as \( AC \) congruent to \( DF \).
Depending on the specific angles in triangles \( ABC \) and \( DEF \) that are already known, the congruent side needed would properly align.
Therefore, at least one option needed to use AAS is **AC is congruent to DF**.
To finalize:
1. If you already have two angles known in both triangles, selecting **AB is congruent to DE** can also be used depending on which angles you know, but direct references to corresponding angles help clarify congruence.
So the option:
- **AB is congruent to DE** (if it connects with one known angle) or
- **AC is congruent to DF** (best fits in aligning with the mentioned angles)
Thus, you would need either **AC is congruent to DF** or **one corresponding angle congruence** which is not mentioned in your list. It's essential to confirm with the specific angles to draw a definitive conclusion.