Question
When mapping △DEF onto △JKL to prove they are congruent, which of the following options identifies a pair of corresponding parts that are also congruent? Option #1: ∠F≅∠J Option #2: DF¯¯¯¯¯¯¯¯≅KL¯¯¯¯¯¯¯¯ Option #3: ∠D≅∠L Option #4: DE¯¯¯¯¯¯¯¯≅JK¯¯¯¯¯¯¯¯ (1 point) Option # identifies a pair of congruent corresponding parts.
Answers
GPT-4o mini
To prove that triangles △DEF and △JKL are congruent, you'll want to identify corresponding parts, which include sides and angles, that are congruent in each triangle.
Based on the options you've provided, if you are mapping △DEF onto △JKL, the corresponding angles and sides must match up.
Here is a typical correspondence:
- ∠D corresponds to ∠J
- ∠E corresponds to ∠K
- ∠F corresponds to ∠L
- DE corresponds to JK
- DF corresponds to KL
- EF corresponds to JL
Let's analyze the options:
1. **Option #1: ∠F≅∠J** — This suggests F corresponds with J, which is not typically correct based on standard naming conventions.
2. **Option #2: DF≅KL** — This suggests DF corresponds with KL, which is valid.
3. **Option #3: ∠D≅∠L** — This suggests D corresponds with L, which is not typically the case based on standard naming conventions.
4. **Option #4: DE≅JK** — This suggests DE corresponds with JK, which is also valid.
Based on typical triangle naming conventions, **Option #2** (DF≅KL) is a pair of corresponding congruent parts, as well as **Option #4** (DE≅JK).
If only one option must be identified, select Option #2 or Option #4, as both are valid matches for corresponding parts of congruent triangles. If the task permits only a single choice and you have to select one, you might go with Option #2.
Based on the options you've provided, if you are mapping △DEF onto △JKL, the corresponding angles and sides must match up.
Here is a typical correspondence:
- ∠D corresponds to ∠J
- ∠E corresponds to ∠K
- ∠F corresponds to ∠L
- DE corresponds to JK
- DF corresponds to KL
- EF corresponds to JL
Let's analyze the options:
1. **Option #1: ∠F≅∠J** — This suggests F corresponds with J, which is not typically correct based on standard naming conventions.
2. **Option #2: DF≅KL** — This suggests DF corresponds with KL, which is valid.
3. **Option #3: ∠D≅∠L** — This suggests D corresponds with L, which is not typically the case based on standard naming conventions.
4. **Option #4: DE≅JK** — This suggests DE corresponds with JK, which is also valid.
Based on typical triangle naming conventions, **Option #2** (DF≅KL) is a pair of corresponding congruent parts, as well as **Option #4** (DE≅JK).
If only one option must be identified, select Option #2 or Option #4, as both are valid matches for corresponding parts of congruent triangles. If the task permits only a single choice and you have to select one, you might go with Option #2.