Question
Example: What else is needed?
In the following diagram, C is the midpoint of BD and ∠ACBZECD. What additional piece of information would you need to be able to state that △ABC=AEDC by the SAS Congruence Theorem?
B
E
A
D
MULTIPLE-CHOICE QUESTION
What does that mean about BC and DC?
(select all that apply)
They will be perpendicular
They will be parallel
They will be equal in lengths
They will be congruent
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In the following diagram, C is the midpoint of BD and ∠ACBZECD. What additional piece of information would you need to be able to state that △ABC=AEDC by the SAS Congruence Theorem?
B
E
A
D
MULTIPLE-CHOICE QUESTION
What does that mean about BC and DC?
(select all that apply)
They will be perpendicular
They will be parallel
They will be equal in lengths
They will be congruent
Rewatch
Submit
Answers
Answered by
GPT-4o mini
To determine how to apply the SAS Congruence Theorem to triangles \( \triangle ABC \) and \( \triangle AEDC \) in your scenario, we need to establish:
1. That two sides of the triangles are equal in length (which is often established through midpoints or given lengths).
2. That the angle included between those two sides is equal.
Given the information provided (that \( C \) is the midpoint of \( BD \) and that \( \angle ACB \cong \angle ECD \)), we now need to ensure that one additional side length is equal.
### What additional piece of information would you need?
To state that \( \triangle ABC \cong \triangle AEDC \) by the SAS Congruence Theorem, you would need to know that:
- \( BC = DC \)
### Regarding \( BC \) and \( DC \):
For the multiple-choice question about what this means about \( BC \) and \( DC \):
- **They will be equal in lengths**: **True** — This is what we need for SAS congruence.
- **They will be congruent**: **True** — Congruent means equal in lengths.
- **They will be perpendicular**: **False** — Perpendicularity is not required for the SAS criterion.
- **They will be parallel**: **False** — Parallel lines do not apply directly in this context of triangle congruency.
### Summary of correct choices:
- They will be equal in lengths
- They will be congruent
By confirming that \( BC \) and \( DC \) are equal, we can apply the SAS Congruence Theorem since we already know the included angle and one side of each triangle (based on \( C \) being the midpoint).
1. That two sides of the triangles are equal in length (which is often established through midpoints or given lengths).
2. That the angle included between those two sides is equal.
Given the information provided (that \( C \) is the midpoint of \( BD \) and that \( \angle ACB \cong \angle ECD \)), we now need to ensure that one additional side length is equal.
### What additional piece of information would you need?
To state that \( \triangle ABC \cong \triangle AEDC \) by the SAS Congruence Theorem, you would need to know that:
- \( BC = DC \)
### Regarding \( BC \) and \( DC \):
For the multiple-choice question about what this means about \( BC \) and \( DC \):
- **They will be equal in lengths**: **True** — This is what we need for SAS congruence.
- **They will be congruent**: **True** — Congruent means equal in lengths.
- **They will be perpendicular**: **False** — Perpendicularity is not required for the SAS criterion.
- **They will be parallel**: **False** — Parallel lines do not apply directly in this context of triangle congruency.
### Summary of correct choices:
- They will be equal in lengths
- They will be congruent
By confirming that \( BC \) and \( DC \) are equal, we can apply the SAS Congruence Theorem since we already know the included angle and one side of each triangle (based on \( C \) being the midpoint).