Question
Essay
Your teacher will grade your response for the following question to ensure that you receive proper credit for your answer.
What are the missing reasons in the proof?
Given: parallelogram upper A upper B upper C upper D with diagonal modifying above upper B upper D with bar
Prove: triangle upper A upper B upper D congruent to triangle upper C upper D upper B
Parallelogram upper A upper B upper C upper D is shown with diagonal segment upper B upper D drawn.
A partially completed two column proof is given with the first column titled 'Statements' and the second column titled 'Reasons.'
The first column contains:
1 period modifying above upper A upper D with bar parallel to modifying above upper B upper C with bar
2 period angle upper A upper D upper B congruent to angle upper C upper B upper D
3 period modifying above upper A upper B with bar parallel to modifying above upper C upper D with bar
4 period angle upper A upper B upper D congruent to angle upper C upper D upper B
5 period modifying above upper D upper B with bar congruent to modifying above upper D upper B with bar
6 period triangle upper A upper B upper D congruent to triangle upper C upper D upper B
The second column contains:
1 period Definition of parallelogram
2 period Alternate Interior Angles Theorem
3 period question-mark
4 period question-mark
5 period question-mark
6 period question-mark
(4 points)
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Your teacher will grade your response for the following question to ensure that you receive proper credit for your answer.
What are the missing reasons in the proof?
Given: parallelogram upper A upper B upper C upper D with diagonal modifying above upper B upper D with bar
Prove: triangle upper A upper B upper D congruent to triangle upper C upper D upper B
Parallelogram upper A upper B upper C upper D is shown with diagonal segment upper B upper D drawn.
A partially completed two column proof is given with the first column titled 'Statements' and the second column titled 'Reasons.'
The first column contains:
1 period modifying above upper A upper D with bar parallel to modifying above upper B upper C with bar
2 period angle upper A upper D upper B congruent to angle upper C upper B upper D
3 period modifying above upper A upper B with bar parallel to modifying above upper C upper D with bar
4 period angle upper A upper B upper D congruent to angle upper C upper D upper B
5 period modifying above upper D upper B with bar congruent to modifying above upper D upper B with bar
6 period triangle upper A upper B upper D congruent to triangle upper C upper D upper B
The second column contains:
1 period Definition of parallelogram
2 period Alternate Interior Angles Theorem
3 period question-mark
4 period question-mark
5 period question-mark
6 period question-mark
(4 points)
Skip to navigation
Answers
GPT 3.5
To complete the missing reasons in the proof, we need to provide justifications for statements 3, 4, 5, and 6.
Possible reasons for statement 3 could be:
3. Parallel lines cut by a transversal form congruent alternate interior angles.
Possible reasons for statement 4 could be:
4. Corresponding angles of parallel lines are congruent.
Possible reasons for statement 5 could be:
5. A segment is congruent to itself.
Possible reasons for statement 6 could be:
6. If two triangles have congruent corresponding angles and a congruent included side, then the triangles are congruent (ASA Congruence Theorem).
Possible reasons for statement 3 could be:
3. Parallel lines cut by a transversal form congruent alternate interior angles.
Possible reasons for statement 4 could be:
4. Corresponding angles of parallel lines are congruent.
Possible reasons for statement 5 could be:
5. A segment is congruent to itself.
Possible reasons for statement 6 could be:
6. If two triangles have congruent corresponding angles and a congruent included side, then the triangles are congruent (ASA Congruence Theorem).