Question

geometry
checkpoint #3 review (1.1 - 1.1 & 1.2)
name:
directions: draw and label an example of each of the following descriptions below.

1. an angle formed by (overrightarrow{vx}) and (overrightarrow{vz})
2. a line that contains points a, b, c, and d
3. (overline{ab}perpoverline{ef})
4. a ray with endpoint m and goes through point n

determine if the following questions are true or false.

1. the intersection of two planes is a line. true false
2. you need at least three points to create a line. true false
3. an angle is two rays with a common endpoint. true false
4. a line is two - dimensional. true false
5. (overrightarrow{ab}) could be read

ay ab\ or
ay ba\. true false

1. (overline{ab}) could be read \line ab\ or \line ba\. true false
2. (angle abc) is the same as (angle bca). true false

answer the following questions in regards to the given diagram. be sure to use the correct notations.

1. name three coplanar points.
2. name three collinear points.
3. name two parallel lines.
4. name two skew lines.
5. name an angle in two ways.

Explanation:

Step1: Recall geometry facts

1. The intersection of two planes is a line. This is a fundamental geometric concept, so it's TRUE.

Step2: Analyze line - point relationship

A line can be created with two points. So the statement "You need at least three points to create a line" is FALSE.

Step3: Recall angle definition

An angle is formed by two rays with a common endpoint. So this is TRUE.

Step4: Understand line properties

A line is one - dimensional. So the statement "A line is two - dimensional" is FALSE.

Step5: Analyze ray notation

A ray $\overrightarrow{AB}$ has endpoint $A$ and goes through $B$, while $\overrightarrow{BA}$ has endpoint $B$ and goes through $A$. They are different rays. So the statement "$\overrightarrow{AB}$ could be read 'ray AB' or 'ray BA'" is FALSE.

Step6: Analyze line notation

A line $\overleftrightarrow{AB}$ can be read "line AB" or "line BA" since a line has no direction. So this is TRUE.

Step7: Analyze angle notation

$\angle ABC$ has vertex $B$ and the rays $\overrightarrow{BA}$ and $\overrightarrow{BC}$, while $\angle BCA$ has vertex $C$ and the rays $\overrightarrow{CB}$ and $\overrightarrow{CA}$. They are different angles. So the statement "$\angle ABC$ is the same as $\angle BCA$" is FALSE.

Step8: For coplanar points

Points that lie on the same plane. For example, points $A$, $B$, $C$ are coplanar (assuming they are on the same face of the cube - like figure).

Step9: For collinear points

Points that lie on the same line. For example, if there are three points on an edge of the cube - like figure, say $A$, $X$, $D$ (assuming they are on a straight - line segment).

Step10: For parallel lines

Parallel lines are lines in the same plane that do not intersect. For example, $AB$ and $CD$ (assuming they are on the same face and do not intersect).

Step11: For skew lines

Skew lines are non - parallel and non - intersecting lines that do not lie in the same plane. For example, $AB$ and $EH$ (assuming one is on the top - face and the other on the bottom - face and they do not lie in the same plane).

Step12: For naming an angle in two ways

For $\angle BAC$, it can also be named $\angle CAB$.

Answer:

1. TRUE
2. FALSE
3. TRUE
4. FALSE
5. FALSE
6. TRUE
7. FALSE
8. A, B, C (answers may vary)
9. A, X, D (answers may vary)
10. AB, CD (answers may vary)
11. AB, EH (answers may vary)
12. $\angle BAC$, $\angle CAB$ (answers may vary)