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Worksheet: Analyzing Statements Using Postulates

Q1:

Determine whether the following is true or false: the vertices of a triangle determine a plane.

  • Atrue
  • Bfalse

Q2:

Determine whether the following is true or false: the vertices of a parallelogram do not determine a plane.

  • Afalse
  • Btrue

Q3:

Complete using one of the choices below: If two planes have two common points 𝐴 and 𝐡 , then they .

  • Aintersect at a straight line parallel to βƒ–     βƒ— 𝐴 𝐡
  • Bare coincident
  • Chave a third point in common, which does not belong to βƒ–     βƒ— 𝐴 𝐡
  • Dintersect at βƒ–     βƒ— 𝐴 𝐡

Q4:

Are points 𝑇 , 𝑆 , 𝑅 , 𝑄 , and 𝑉 coplanar?

  • Ano
  • Byes

Q5:

Which of the following statements is true about the two planes?

  • A The two planes are coincident.
  • B The two planes are intersected.
  • C The two planes are parallel.

Q6:

How many planes can pass through two different points?

  • A1
  • B2
  • C0
  • Dan infinite number

Q7:

How many planes can pass through three collinear points?

  • A1
  • B2
  • C3
  • Dan infinite number

Q8:

Determine whether the following sentence is true or false: Any three points in a space determine a plane.

  • A false
  • B true

Q9:

Determine whether the following sentence is true or false: If 𝐴 𝐡 𝐢 𝐷 is a quadrilateral, then there is only one plane passing through all of its sides.

  • A true
  • B false

Q10:

What does it mean for two lines to be considered skew?

  • AThey are not coincident.
  • BThey are not parallel.
  • CThey are located in the same plane.
  • DThey are not located in the same plane.

Q11:

In gymnastics, the floor exercises are done on a mat that is 40 feet long and 40 feet wide. Is the mat an example of a point, a line, a line segment, or part of a plane?

  • A a line
  • B a point
  • C a line segment
  • D part of a plane

Q12:

If 𝑋 and π‘Œ are two planes, where 𝑋 ∩ π‘Œ = βˆ… , what is the relation between those two planes?

  • AThey are coincident.
  • BThey intersect each other.
  • CThey are parallel to each other.

Q13:

Which of the following statements is true about the two planes?

  • A The two planes are parallel.
  • B The two planes are intersected.
  • C The two planes are coincident.

Q14:

Consider three intersecting planes. The normals to each of the planes are coplanar. Are the lines of intersection parallel?

  • A Yes
  • B No

Q15:

The given figure shows a pentagonal prism placed on a plane 𝐴 . Determine whether plane 𝑀 𝑁 𝑃 and plane 𝐴 intersect.

  • Ano
  • Byes

Q16:

Is this true or false?

A plane figure is two-dimensional (2D).

  • A true
  • B false