Question
The diagram shows several points and lines.
4 intersecting lines are shown. A horizontal line contains points K, N, R. A vertical line contains points M, N, Q. Another line intersects the lines at points K and M. Another line has points J, K, and Q. Points L and P are not on the lines.
Which statements are true based on the diagram? Select two options.
Points K, M, and N are collinear.
Points J, K, and Q are collinear.
Point R is the intersection of line KN and line MQ.
Lines JQ, KM, and MQ all intersect at point K.
There is only one line that can be drawn through points L and P.
What is the format of this proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABD is a right angle
A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.
A 2-column table has 8 rows. The first column is labeled Statements with entries angle A B C is a right angle, angle D B C is a straight angle, m angle A B C = 90 degrees, m angle D B C = 180 degrees, m angle A B D + m angle A B C = m angle D B C, m angle A B D + 90 degrees = 180 degrees, m angle A B D = 90 degrees, angle A B C is-congruent-to angle A B D. The second column is labeled Reasons with entries, given, given, definition of right angle, definition of straight angle, angle addition property, substitution property, subtraction property, and definition of right angle.
two-column proof
two-paragraph proof
flowchart proof
one-paragraph proof
3 lines are shown. A line with points P, R, N intersects a line with points M, R, O at point R. A line extends from point R to point L between angle P R M.
Which angles form a linear pair?
AnglePRL and AngleLRM
AngleORP and AngleMRN
AngleMRN and AngleNRO
AngleLRP and AngleORP
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
A line contains point A, B, C.
A 2-column table has 6 rows. Column 1 is labeled Statements with entries line segment A B is-congruent-to line segment B C, line segment B C is congruent to line segment E F, line segment A B is-congruent-to line segment E F, A B = E F, E G = E F + F G, E G = A B + F G. Column 2 is labeled reasons with entries given, given, transitive property, definition of congruent segments, segment addition, and substitution.
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
Which statements are true based on the diagram? Select three options.
Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y.
4 intersecting lines are shown. A horizontal line contains points K, N, R. A vertical line contains points M, N, Q. Another line intersects the lines at points K and M. Another line has points J, K, and Q. Points L and P are not on the lines.
Which statements are true based on the diagram? Select two options.
Points K, M, and N are collinear.
Points J, K, and Q are collinear.
Point R is the intersection of line KN and line MQ.
Lines JQ, KM, and MQ all intersect at point K.
There is only one line that can be drawn through points L and P.
What is the format of this proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABD is a right angle
A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.
A 2-column table has 8 rows. The first column is labeled Statements with entries angle A B C is a right angle, angle D B C is a straight angle, m angle A B C = 90 degrees, m angle D B C = 180 degrees, m angle A B D + m angle A B C = m angle D B C, m angle A B D + 90 degrees = 180 degrees, m angle A B D = 90 degrees, angle A B C is-congruent-to angle A B D. The second column is labeled Reasons with entries, given, given, definition of right angle, definition of straight angle, angle addition property, substitution property, subtraction property, and definition of right angle.
two-column proof
two-paragraph proof
flowchart proof
one-paragraph proof
3 lines are shown. A line with points P, R, N intersects a line with points M, R, O at point R. A line extends from point R to point L between angle P R M.
Which angles form a linear pair?
AnglePRL and AngleLRM
AngleORP and AngleMRN
AngleMRN and AngleNRO
AngleLRP and AngleORP
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
A line contains point A, B, C.
A 2-column table has 6 rows. Column 1 is labeled Statements with entries line segment A B is-congruent-to line segment B C, line segment B C is congruent to line segment E F, line segment A B is-congruent-to line segment E F, A B = E F, E G = E F + F G, E G = A B + F G. Column 2 is labeled reasons with entries given, given, transitive property, definition of congruent segments, segment addition, and substitution.
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
Which statements are true based on the diagram? Select three options.
Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y.
Answers
GPT-4o mini
Based on your descriptions, here are the answers to your questions:
### 1. True Statements Based on the Diagram:
**Select two options:**
1. **Points J, K, and Q are collinear.**
2. **Lines JQ, KM, and MQ all intersect at point K.**
### 2. Format of the Proof:
The format of the proof you've described is a **two-column proof.**
### 3. Angles that Form a Linear Pair:
**Which angles form a linear pair?**
1. **Angle PRL and Angle LRM.**
### 4. Part of the Proof:
**Which part of the proof does the fourth statement and reason represent?**
- **It is part of the argument.**
### 5. True Statements Based on the Diagram of Planes:
**Select three options:**
1. **Line z intersects plane S at point C.**
2. **The line containing points A and B lies entirely in plane T.**
3. **Planes R and T intersect at line y.**
Please verify each answer based on your understanding of the diagrams you are referring to, as selections are based on the descriptions provided!
### 1. True Statements Based on the Diagram:
**Select two options:**
1. **Points J, K, and Q are collinear.**
2. **Lines JQ, KM, and MQ all intersect at point K.**
### 2. Format of the Proof:
The format of the proof you've described is a **two-column proof.**
### 3. Angles that Form a Linear Pair:
**Which angles form a linear pair?**
1. **Angle PRL and Angle LRM.**
### 4. Part of the Proof:
**Which part of the proof does the fourth statement and reason represent?**
- **It is part of the argument.**
### 5. True Statements Based on the Diagram of Planes:
**Select three options:**
1. **Line z intersects plane S at point C.**
2. **The line containing points A and B lies entirely in plane T.**
3. **Planes R and T intersect at line y.**
Please verify each answer based on your understanding of the diagrams you are referring to, as selections are based on the descriptions provided!