Lesson 2 unit 2
Points, lines, planes
1. Any three points must be _____
C. Coplanar
2. An axiom or a _____ is an accepted statement of fact.
C. Postulate
3. In geometry, _____ is the set of all points.
D. Space
4. Look at the figure points C,D,E, and G are _____ points.
C. Coplanar
5. Through any two points there is exactly one ______
A. Line
6. Look at the figure. What is another point that is coplanar with points D,E, and G?
B. C
7. Look at the figure. Which point is coplanar with points B,C, and H?
D. G. <--->
8. Look at the figure. RS is the intersection of plain ____ and plane QRST.
B. RSWV
9. Look at the figure. What is another name for m?
B. <---->
AC
10. Look at the figure. What is another way of naming line m?
A. <---->
AB
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To answer the questions:
1. Any three points must be Coplanar.
To understand this, we need to know the definition of coplanar. In geometry, coplanar means that points or lines lie in the same plane. So, any three points lying in the same plane would be coplanar.
2. An axiom or a Postulate is an accepted statement of fact.
To know this, we need to understand what an axiom or postulate means in geometry. Axioms or postulates are basic statements or principles that are accepted without proof and used as a basis for reasoning in geometry.
3. In geometry, Space is the set of all points.
The concept of "space" in geometry refers to the set of all points. It includes every point, line, and shape that can exist in three-dimensional space.
4. In the given figure, points C, D, E, and G are Coplanar points.
Looking at the figure, if all the points lie in the same plane, then they are coplanar. Therefore, points C, D, E, and G are coplanar.
5. Through any two points, there is exactly one Line.
This is a fundamental concept in geometry. A line is determined by any two distinct points. So, for any two points, there is a unique line that passes through them.
6. Another point that is coplanar with points D, E, and G is C.
To find another point that is coplanar with D, E, and G, we need to look for a point that lies in the same plane. In this case, point C satisfies this condition and is therefore coplanar with D, E, and G.
7. The point that is coplanar with points B, C, and H is G.
To find the point that is coplanar with B, C, and H, we need to look for a point that lies in the same plane. In this case, point G satisfies this condition and is therefore coplanar with B, C, and H.
8. RS is the intersection of plane RSWV and plane QRST.
To determine the plane of intersection, we need to find the common points between the two given planes. In this case, RS is the common line between plane RSWV and plane QRST, making RS the intersection of those two planes.
9. In the given figure, the name for m is AC.
To name a line, we usually use two points on that line. In this case, the line m is named using the points A and C, so the name for m is AC.
10. Another way of naming line m is AB.
In the given figure, line m passes through points A and B. Therefore, another way to name line m is using the points A and B, making the name AB.
Keep in mind that these answers are based on the information provided and the understanding of geometry principles.