points, lines and planes. prerequisite skills copy and complete the statement. 1. the distance...
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Points, Lines and Points, Lines and PlanesPlanes
Points, Lines and Points, Lines and PlanesPlanes
Prerequisite Skills
Copy and complete the statement.
1. The distance around a rectangle is called its ? , and the distance around a circle is called its ? .
ANSWER perimeter, circumference
2. The number of square units covered by a figure is called its ? .
ANSWER area
VOCABULARY CHECK
Prerequisite Skills SKILLS AND ALGEBRA CHECK
Evaluate the expression.
3.
|4 – 6|
4. |3 – 11|
5. |–4 + 5|
6. |–8 – 10|
ANSWER 2
ANSWER 8
ANSWER 1
ANSWER 18
Prerequisite Skills SKILLS AND ALGEBRA CHECK
Evaluate the expression when x = 2.
7.
5x
8. 20 – 8x
9. –18 + 3x
10. –5x – 4 + 2x
ANSWER 10
ANSWER 4
–12ANSWER
–10ANSWER
Prerequisite Skills SKILLS AND ALGEBRA CHECK
Solve the equation.
11.
274 = –2z
12. 8x + 12 = 60 ANSWER 6
13. 2y – 5 + 7y = –32 ANSWER –3
–137ANSWER
Prerequisite Skills SKILLS AND ALGEBRA CHECK
14.
6p + 11 +3p = –7
15. 8m – 5 = 25 – 2m ANSWER 3
16. –2n + 18 = 5n – 24 ANSWER 6
Solve the equation.
–2ANSWER
SOLUTION
EXAMPLE 1 Name points, lines, and planes
b. Name three points that are collinear.Name four points that are coplanar.
a. Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.
a. Give two other names for PQ and for plane R.
EXAMPLE 1 Name points, lines, and planes
b. Points S, P, and T lie on the same line, so they are collinear. Points S, P, T,and V lie in the same plane, so they are coplanar.
GUIDED PRACTICE for Example 1
ANSWER
Other names for ST are TS and PT. Point V is not coplanar with points Q,S and T
1. Use the diagram in Example 1. Give two other names for ST . Name a point that is not coplanar with points Q, S, and T.
EXAMPLE 2 Name segments, rays, and opposite rays
b. Name all rays with endpoint J . Which of these rays are opposite rays?
SOLUTION
a. Another name for GH is HG .
b. The rays with endpoint J are JE , JG , JF , and JH . The pairs of opposite rays with endpoint J are JE and JF , and JG and JH .
a. Give another name for GH .
GUIDED PRACTICE for Example 2
3. Are HJ and JH the same ray ? Are HJ and HG the same ray? Explain.
ANSWER
Another name for EF is FE
ANSWER
No; HJ and JH have different endpoints, so they are not the same ray
Yes; points J and G lie on the same side of H, so they are the same ray
2. Give another name for EF
EXAMPLE 3 Sketch intersections of lines and planes
a. Sketch a plane and a line that is in the plane.
b. Sketch a plane and a line that does not intersect the plane.
c. Sketch a plane and a line that intersects the plane at a point.
SOLUTION
a. b. c.
EXAMPLE 4 Sketch intersections of planes
Sketch two planes that intersect in a line.
SOLUTION
Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden.
STEP 2
Draw: the line of intersection.STEP 3
Draw: a vertical plane. Shade the plane.
STEP 1
GUIDED PRACTICE for Examples 3 and 4
4. Sketch two different lines that intersect a plane at the same point.
Use the diagram at the right.
5. Name the intersection of PQ and line k.
ANSWER Point M
ANSWER
GUIDED PRACTICE for Examples 3 and 4
6. Name the intersection of plane A and plane B.
7. Name the intersection of line k and plane A.
ANSWER Line K
ANSWER Line K