assignment - unit 1 review
1. what is the intersection of two planes?
2. what is the intersection of two lines?
3. what is the intersection of a line & a plane?
4. state the segment addition postulate using point \a\ lies between p & t.
5. state the angle addition postulate using point t lies in the interior of ∠bad
6. how many lines can contain two distinct points?
7. a plane contains at least ____ noncollinear points.
8. if two points are in the same plane, then the ____ containing them is in the same plane.
9. in geometry, the three basic undefined terms are ____, ____, and ____
10. through any two points, there is exactly one ____
11. if two angles form a linear pair, then they are ____ & ____ angles
12. a line segment contains ____ endpoint(s).
13. a ray contains ____ endpoint(s).
14. a line contains ____ endpoint(s).
15. give the symbol for the segment with endpoints d and p
16. give the symbol for the line containing points o and l
17. give the symbol for the ray with endpoint t moving infinitely in the direction of z
18. make a sketch and find the indicated measurements.
a, b, and c are collinear. b is between a and c.
ab = 3x + 4, bc = 2x - 1 and ac = 18.
(a) ... (b) ... (c) ... (d) ...

Question

Accepted Answer

### Question 1: What is the intersection of two planes?
# Brief Explanations:
In geometry, when two planes intersect, their intersection is a line. This is a fundamental concept in the study of planes and their intersections.
# Answer: A line

### Question 2: What is the intersection of two lines?
# Brief Explanations:
In geometry, two distinct lines (in a plane) either intersect at a single point or are parallel (and thus do not intersect). For two lines that are not parallel, their intersection is a single point.
# Answer: A point

### Question 3: What is the intersection of a line & a plane?
# Brief Explanations:
A line and a plane can intersect in one of three ways: the line lies entirely in the plane (infinite intersection points), the line is parallel to the plane (no intersection), or the line intersects the plane at a single point. In the general case (not parallel and not contained), the intersection is a point.
# Answer: A point (or the line if the line is in the plane)

### Question 4: State the segment addition postulate using point "A" lies between P & T.
# Brief Explanations:
The segment addition postulate states that if a point lies between two other points on a line segment, then the sum of the lengths of the two smaller segments is equal to the length of the larger segment. So if A is between P and T, then $ PA + AT = PT $.
# Answer: $ PA + AT = PT $

### Question 5: State the angle addition postulate using point T lies in the interior of $ \angle BAD $
# Brief Explanations:
The angle addition postulate states that if a point lies in the interior of an angle, then the sum of the measures of the two smaller angles formed is equal to the measure of the larger angle. So if T is in the interior of $ \angle BAD $, then $ \angle BAT + \angle TAD = \angle BAD $.
# Answer: $ \angle BAT + \angle TAD = \angle BAD $

### Question 6: How many lines can contain two distinct points?
# Brief Explanations:
By the postulate of a line, through any two distinct points, there is exactly one line. This is a fundamental geometric postulate.
# Answer: One

### Question 7: A plane contains at least ______ noncollinear points.
# Brief Explanations:
A plane is defined as a flat, two - dimensional surface that extends infinitely far. By the definition of a plane, a plane contains at least three non - collinear points (points that do not lie on the same line).
# Answer: Three

### Question 8: If two points are in the same plane, then the ______ containing them is in the same plane.
# Brief Explanations:
By the postulate of a line and a plane, if two points are in a plane, the line containing those two points lies entirely within that plane.
# Answer: Line

### Question 9: In geometry, the three basic undefined terms are ______, ______, and ______
# Brief Explanations:
In geometry, the three basic undefined terms are point (which has no size, only a location), line (which is a straight path that extends infinitely in both directions), and plane (which is a flat surface that extends infinitely in all directions).
# Answer: Point, Line, Plane

### Question 10: Through any two points, there is exactly one ______
# Brief Explanations:
This is a fundamental postulate in geometry. Through any two distinct points, there is exactly one line.
# Answer: Line

### Question 11: If two angles form a linear pair, then they are ______ & ______ angles
# Brief Explanations:
A linear pair of angles is formed when two adjacent angles form a straight line. So, if two angles form a linear pair, they are adjacent (share a common side and vertex) and supplementary (their sum is $ 180^{\circ} $).
# Answer: Adjacent, Supplementary

### Question 12: A line segment contains ______ endpoint(s)
# Brief Explanations:
A line segment is a part of a line that is bounded by two distinct endpoints. So a line segment has two endpoints.
# Answer: Two

### Question 13: A ray contains ______ endpoint(s)
# Brief Explanations:
A ray is a part of a line that starts at a point (the endpoint) and extends infinitely in one direction. So a ray has one endpoint.
# Answer: One

### Question 14: A line contains ______ endpoint(s)
# Brief Explanations:
A line is a straight path that extends infinitely in both directions, so it has no endpoints.
# Answer: Zero

### Question 15: Give the symbol for the segment with endpoints D and P
# Brief Explanations:
The symbol for a line segment with endpoints D and P is $ \overline{DP} $ (or $ \overline{PD} $, since the order of the endpoints does not matter for the segment).
# Answer: $ \overline{DP} $

### Question 16: Give the symbol for the line containing points O and L
# Brief Explanations:
The symbol for a line containing points O and L is $ \overleftrightarrow{OL} $ (or $ \overleftrightarrow{LO} $, as the order of the points does not matter for the line).
# Answer: $ \overleftrightarrow{OL} $

### Question 17: Give the symbol for the ray with endpoint T moving infinitely in the direction of Z
# Brief Explanations:
The symbol for a ray with endpoint T and going through Z (extending infinitely in the direction of Z) is $ \overrightarrow{TZ} $.
# Answer: $ \overrightarrow{TZ} $

### Question 18:
Given that A, B, and C are collinear, B is between A and C, $ AB = 3x + 4 $, $ BC=2x - 1 $ and $ AC = 18 $

#### Part (a): Find the value of x
# Explanation:
## Step 1: Apply the segment addition postulate
Since B is between A and C, we know that $ AB+BC = AC $. Substitute the given expressions: $ (3x + 4)+(2x - 1)=18 $
## Step 2: Simplify the left - hand side
Combine like terms: $ 3x+2x + 4-1=18 $, which simplifies to $ 5x+3 = 18 $
## Step 3: Solve for x
Subtract 3 from both sides: $ 5x=18 - 3=15 $. Then divide both sides by 5: $ x=\frac{15}{5}=3 $
# Answer: $ x = 3 $

#### Part (b): Find the length of AB
# Explanation:
## Step 1: Substitute x into the expression for AB
We know that $ AB = 3x + 4 $ and $ x = 3 $. So $ AB=3\times3 + 4 $
## Step 2: Calculate the value
$ 3\times3+4=9 + 4=13 $
# Answer: $ AB = 13 $

#### Part (c): Find the length of BC
# Explanation:
## Step 1: Substitute x into the expression for BC
We know that $ BC = 2x-1 $ and $ x = 3 $. So $ BC=2\times3-1 $
## Step 2: Calculate the value
$ 2\times3 - 1=6 - 1=5 $
# Answer: $ BC = 5 $

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QUESTION IMAGE

Question

Explanation:

Question 1: What is the intersection of two planes?

Answer:

Question 2: What is the intersection of two lines?