LESSON 1.1 Practice A For use with pages 2-8 In Exercises 1-8, use the diagram. 1. Give two other names for AB. 2. Name three points that are collinear. 3. Give another name for plane F. 4. Name a point that is not coplanar with A, B, and C. 5. Give another name for CD. 6. Name three rays with endpoint B. 7. Name a pair of opposite rays. 8. Give another name for CD. Sketch the figure described. 9. Three points that are collinear E A 49 36 C B 10. Four points that are coplanar h None
iv 6 LESSON 1.1 Name LESSON 1.1 Practice A For use with pages 2-8 In Exercises 1-8, use the diagram. 1. Give two other names for AB. 2. Name three points that are collinear. 3. Give another name for plane F. 4. Name a point s not coplanar with A, B, and C. 5. Give another name for CD. 6. Name three rays with endpoint B. 7. Name a pair of opposite rays. 8. Give another name for CD. Sketch the figure described. 9. Three points that are collinear 11. Three lines that intersect at one point In Exercises 13-20, use the diagram. 13. Are points J, K, and L collinear? 14. Are points J, K, and L coplanar? 15. Are points J, K, and M collinear? 16. Are points J, K, and M coplanar? 17. Name the intersection of KL and PO. 18. Name the intersection of PQ and plane KMN. 19. Name the intersection of plane R and plane S. 20. Name three pairs of opposite rays. Geometry Chapter 1 Resource Book Date K E M A I C B 10. Four points that are coplanar D 12. A line and a plane that intersect at one point h 1 1 R Copyright © hv McDonal Littalla divinion of m Use of this card is subject to the
The correct answer and explanation is:
To answer the questions based on a geometry diagram (as described in a textbook), I’ll first interpret the questions and provide both answers and explanations. Since the exact diagram isn’t provided, I’ll make assumptions about typical geometry diagrams to explain the concepts.
Answers and Explanations:
1. Give two other names for line AB.
- Answer: Line BA, Line EF (if AB is part of line EF, as lines have infinite length in both directions).
- Explanation: Lines can be named using any two points on the line, as the order of the points does not matter. Naming it BA simply reverses the order, while EF might refer to the same line if other points are also collinear with A and B.
2. Name three points that are collinear.
- Answer: Points A, B, and C (assuming they lie on the same straight line).
- Explanation: Collinear points are points that lie on the same straight line. Based on the diagram, any three points lying on the same line are collinear.
3. Give another name for plane F.
- Answer: Plane ABC (if A, B, and C are points in the plane).
- Explanation: Planes can be named using three non-collinear points in the plane or by a designated letter, such as “F.” If A, B, and C are non-collinear and in plane F, then “Plane ABC” is another valid name.
4. Name a point that is not coplanar with A, B, and C.
- Answer: Point D (if it does not lie in plane F with A, B, and C).
- Explanation: Points not coplanar with others do not lie on the same plane. In 3D space, such points appear “above” or “below” the defined plane.
5. Give another name for line CD.
- Answer: Line DC.
- Explanation: Like lines AB and BA, reversing the order of the points names the same line.
6. Name three rays with endpoint B.
- Answer: Ray BA, Ray BC, Ray BD.
- Explanation: A ray starts at a specific endpoint and extends infinitely in one direction. Rays with endpoint B can be named using B and any other point defining their direction.
7. Name a pair of opposite rays.
- Answer: Ray BA and Ray BC (if A, B, and C are collinear, with B between A and C).
- Explanation: Opposite rays share an endpoint and extend in opposite directions, forming a straight line.
8. Give another name for line CD.
- Answer: Line DC (repeating, as this is the same as Question 5).
- Explanation: Lines can be named using either order of two points defining them.
Sketches:
9. Three points that are collinear.
- Draw a straight line with points labeled A, B, and C along it.
10. Four points that are coplanar.
- Draw a parallelogram or rectangle to represent a plane. Place points A, B, C, and D inside the plane.
Explanations in 300 Words:
These exercises assess foundational geometry concepts like collinearity, coplanarity, naming conventions for lines, planes, and rays, as well as the relationships between geometric figures. A line is defined by two points, and its name remains valid regardless of the order of points used. Similarly, a plane can be named using a single letter or any three non-collinear points lying within it.
Collinearity implies points lying on the same straight line, while coplanarity refers to points existing within the same plane. When points are not coplanar, they exist in different spatial planes, creating a 3D perspective.
Rays have a single endpoint and extend infinitely in one direction, making naming dependent on the endpoint and a direction point. Opposite rays share the same endpoint but point in reverse directions, forming a straight line.
These basic principles are essential as they provide a clear understanding of spatial relationships and naming conventions, critical for solving more complex geometry problems. Diagrams are indispensable tools to visualize and solidify these abstract ideas.