Question
Given <q and <4 form a linear pair <2 and <2 are supplementary
1. <1 and <3 form a linear pair 1. Given
2. ___ 2 Linear pair (supplement) theorem
3____ 3 given
4 ___ 4 congruent supplements theorem
5 <2 =~ 5____
6___ 6 transitive property
Geometry
1. <1 and <3 form a linear pair 1. Given
2. ___ 2 Linear pair (supplement) theorem
3____ 3 given
4 ___ 4 congruent supplements theorem
5 <2 =~ 5____
6___ 6 transitive property
Geometry
Answers
Answered by
GPT-4o mini
Based on the information you've provided, it seems that you are forming a proof in geometry using various theorems related to linear pairs, supplementary angles, and congruent angles. Here's how you could fill in the steps:
1. **Given**: ∠q and ∠4 form a linear pair; ∠2 and ∠2 are supplementary.
2. **Linear Pair (Supplement) Theorem**: A linear pair of angles is supplementary. Thus, ∠q + ∠4 = 180°.
3. **Given**: ∠1 and ∠3 form a linear pair.
4. **Congruent Supplements Theorem**: If two angles are supplementary to the same angle (or congruent angles), then those two angles are congruent.
5. **∠2 = ∠5**: Since ∠2 and ∠2 are supplementary, we can express that if ∠4 is supplementary to ∠2, and since ∠4 is also supplementary to ∠5 (a congruent angle from the previous argument), then ∠2 must also equal ∠5.
6. **Transitive Property**: If ∠2 = ∠5 and ∠5 is congruent to ∠6, then ∠2 must also be congruent to ∠6; therefore, we can apply the transitive property.
Here’s how the proof might look completely filled out:
1. **Given**: ∠q and ∠4 form a linear pair; ∠2 and ∠2 are supplementary.
2. **Linear Pair (Supplement) Theorem**: ∠q + ∠4 = 180°.
3. **Given**: ∠1 and ∠3 form a linear pair.
4. **Congruent Supplements Theorem**: Since ∠q and ∠4 are supplementary, and ∠1 is a supplement of ∠3, then ∠3 = ∠4.
5. **Let ∠5 = ∠4** (as the angle that is congruent).
6. **Transitive Property**: If ∠2 + ∠5 = 180° and also ∠2 + ∠2 = 180°, then ∠2 = ∠5.
Make sure to adjust the specific angle names and properties to fit your particular problem as needed!
1. **Given**: ∠q and ∠4 form a linear pair; ∠2 and ∠2 are supplementary.
2. **Linear Pair (Supplement) Theorem**: A linear pair of angles is supplementary. Thus, ∠q + ∠4 = 180°.
3. **Given**: ∠1 and ∠3 form a linear pair.
4. **Congruent Supplements Theorem**: If two angles are supplementary to the same angle (or congruent angles), then those two angles are congruent.
5. **∠2 = ∠5**: Since ∠2 and ∠2 are supplementary, we can express that if ∠4 is supplementary to ∠2, and since ∠4 is also supplementary to ∠5 (a congruent angle from the previous argument), then ∠2 must also equal ∠5.
6. **Transitive Property**: If ∠2 = ∠5 and ∠5 is congruent to ∠6, then ∠2 must also be congruent to ∠6; therefore, we can apply the transitive property.
Here’s how the proof might look completely filled out:
1. **Given**: ∠q and ∠4 form a linear pair; ∠2 and ∠2 are supplementary.
2. **Linear Pair (Supplement) Theorem**: ∠q + ∠4 = 180°.
3. **Given**: ∠1 and ∠3 form a linear pair.
4. **Congruent Supplements Theorem**: Since ∠q and ∠4 are supplementary, and ∠1 is a supplement of ∠3, then ∠3 = ∠4.
5. **Let ∠5 = ∠4** (as the angle that is congruent).
6. **Transitive Property**: If ∠2 + ∠5 = 180° and also ∠2 + ∠2 = 180°, then ∠2 = ∠5.
Make sure to adjust the specific angle names and properties to fit your particular problem as needed!