ASSIGNMENT SOLID MENSURATION
PLANES, LINES AND ANGLES
A. Complete each statement using "Always", "Sometimes", or "Never".
1. Two distinct points are _______ collinear.
2. A line and a point not on the given line are ______ non-coplanar.
3. Three distinct non-collinear points are ______ coplanar.
4. Three points are _____ collinear.
5. Two intersecting lines _______ lie in one plane.
6. Three distinct collinear points are _______ contained in only one plane.
7. Four non-coplanar points _______ determine a space.
8. A line and a plane _________ intersect at a point.
9. Two distinct planes ______ intersect at a line.
10. Two straight lines perpendicular to the same straight line are _______ parallel.
B. Determine the theorem that justifies the following practical applications.
1. Two nails were driven against a wall and a line was drawn to connect them. The line drawn is also on the wall.
2. Karen and Gina were trying to find the location of Manila on the world map. They used the imaginary latitude and longitude lines to do so.
3. Shaggy, a carpenter, decided he had enough of his wobbling four-legged chair and built a three-legged stool that is more suitable.
4. Stan folded his sheet of paper into two and left a crease on where he folded it.
5. Steven, a professional photographer uses tripod for his camera so that he can take picture of his subject better.
C. Solve the following problems completely.
1. How can two pencils (representing lines) be held so that a plane can passed containing both; so that no plane can be passed containing both?
2. What is meant by the statement, "Two planes determine a line" Is this universally true?
3. Can a plane intersect two planes that are not parallel so that the intersections are parallel? Illustrate your answer by passing a plane through the edges of an open book. How must this plane be passed so that the intersections are parallel lines?
4. If two lines do not intersect, can a third line be drawn perpendicular to them?
5. Why are the corner edges of a building perpendicular to the plane of a level street?
6. How many positions can a lightning rod erected at a point occupy w out being vertical? How many positions may it assume and be vertical?
7. In erecting a vertical column a carpenter may use a carpenter square to make certain that the column is perpendicular to the floor. In how in different positions must he places the square against the column to ascertain whether it is vertical? Why?
8. Can a line be perpendicular to both of two planes if they are not parallel?
9. Can one line be perpendicular to two other lines that intersect? Explain.
10. A pole 26 ft. long leans against a wall at a point 10 ft. from the ground. What is the length of the projection of the pole on the ground?