2.4 use postulates and diagrams you will use postulates involving points, lines, and planes....
TRANSCRIPT
2.4 Use Postulates and Diagrams
• You will use postulates involving points, lines, and planes.
• Essential Question: How can you identify postulates illustrated by a diagram?
Warm-Up ExercisesEXAMPLE 1 Identify a postulate illustrated by a diagram
State the postulate illustrated by the diagram.a. b.
SOLUTION
a. Postulate 7: If two lines intersect, then their intersection is exactly one point.
b. Postulate 11: If two planes intersect, then theirintersection is a line.
Warm-Up ExercisesEXAMPLE 2 Identify postulates from a diagram
Use the diagram to write examples of Postulates 9 and 10.
Postulate 9: Plane P contains atleast three noncollinear points,A, B, and C.
Postulate 10: Point A and point B lie in plane P,so line n containing A and B also lies in plane P.
Warm-Up ExercisesGUIDED PRACTICE for Example 1 and 2
Use the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?
1.
ANSWER
Postulate 11
Warm-Up Exercises
Use the diagram in Example 2 to write examples of Postulates 5, 6, and 7.
2.
GUIDED PRACTICE for Example 1 and 2
ANSWER
Postulate 5 : Line n passes through points A and B
Postulate 6 : Line n contains A and B
Postulate 7 : Line m and n intersect at point A
Warm-Up ExercisesEXAMPLE 3 Use given information to sketch a diagram
SOLUTION
STEP 1
Draw TV and label points T and V.
STEP 2Draw point W at the midpoint of TV Mark the congruent segments.
STEP 3Draw PQ through W.
Sketch a diagram showing TV intersecting PQ at point W, so that TW WV .
Warm-Up ExercisesEXAMPLE 4 Interpret a diagram in three dimensions
Which of the following statements cannot be assumed from the diagram?
A, B, and F are collinear.E, B, and D are collinear.AB plane SCD plane TAF intersects BC at point B.
SOLUTION
No drawn line connects E, B, and D, so you cannot assume they are collinear. With no right angle marked, you cannot assume CD plane T.
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
3. If the given information stated PW and QW are congruent, how would you indicate that in the diagram?
In Questions 3 and 4, refer back to Example 3.
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
4. Name a pair of supplementary angles in the
diagram. Explain.
ANSWER
In the diagram the angle TWP and VWP form a linear pair So, angle TWP, VWP are a pair of supplementary angles.
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
5. In the diagram for Example 4, can you assume
plane S intersects plane T at BC ?
ANSWER
Yes
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
6. Explain how you know that AB BC in Example 4.
ANSWER
It is given that line AB is perpendicular to plane S, therefore line AB is perpendicular to every line in the plane that intersect it at point B. So, AB BC
Warm-Up ExercisesDaily Homework Quiz
1. Use the diagram to write an example of Postulate 7.
ANSWER
Line m intersects line n in point F and no other point.
Warm-Up ExercisesDaily Homework Quiz
2. Decide whether the statement “Two planes can intersect in exactly one point R” is true or false. If false, give a reason.
ANSWER
False; Postulate 11 says that if two planes intersect, their intersection is a line.
Warm-Up ExercisesDaily Homework Quiz
Use the diagram to determine if the statement is true or false.
3. The intersection of planes M and N is points B, E and H.
ANSWER
false
Warm-Up ExercisesDaily Homework Quiz
Use the diagram to determine if the statement is true or false.
ANSWER
true
4. GH lies in plane M.
Warm-Up ExercisesDaily Homework Quiz
Use the diagram to determine if the statement is true or false.
ANSWER
false
5. ABE and HED are vertical angles.
• You will use postulates involving points, lines, and planes.
• Essential Question: How can you identify postulates illustrated by a diagram?
• Analyze a diagram to determine what you can assume.• Verify what you can assume by
determining which postulates apply.
You can identify postulates from a diagram by determining which information you can assume. Do not assume congruence, perpendicularity, collinearity, midpoints, and bisectors. Determine which postulate applies.