Parallel — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
Same slope, different intercept.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Slope — How much y changes for each 1 that x increases.
What uses it later
This idea is needed for:
- Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
Practise this idea
36 questions in the course bank use Parallel, in Solving Equations, Length and Area in 2-D Figures, Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Geometric Construction, Measurement. The first 8 are below; the rest are in those units.
Problem 1
Solve 2x + 3 = 2x + 7.
- x = 2
- x = 4
- No solution
- Every number works
Worked answer
No solution
Subtract 2x: 3 = 7
That is false no matter what x is
So there is no solution. The two sides are parallel lines that never meet.
Problem 2
A trapezoid has parallel sides 7 m and 13 m, and height 6 m. Find its area.
Worked answer
60
7 + 132 = 10
10 × 6 = 60 m2
Problem 3
A cube is sliced parallel to one of its faces. What shape is the cross section?
- A square
- A triangle
- A circle
- A hexagon
Worked answer
A square
You get a square identical to the face, no matter how deep you cut.
Problem 4
A cylinder is sliced parallel to its base. What shape is the cross section?
- A rectangle
- A circle
- An oval
- A triangle
Worked answer
A circle
A circle, the same size as the base.
Problem 5
A square pyramid is sliced parallel to its base. What shape is the cross section?
- A triangle
- A square
- A trapezoid
- A pentagon
Worked answer
A square
A square — smaller the higher up you cut.
Problem 6
A cone is sliced parallel to its base. What shape is the cross section?
- A triangle
- A circle
- A trapezoid
- An oval
Worked answer
A circle
A circle — smaller the closer you cut to the tip.
Problem 7
A cube is sliced through the diagonal of its top face and the parallel diagonal of its bottom face. What shape is the cross section?
- A square
- A rectangle
- A triangle
- A hexagon
Worked answer
A rectangle
The plane crosses four faces, so the cross section has four sides
All four corners are right angles, but the horizontal sides are diagonals — longer than the vertical edges
So it is a rectangle, not a square.
Problem 8
A 5 × 4 × 3 rectangular prism is sliced parallel to its 5 × 4 face. Find the area of the cross section.
Worked answer
20
The cross section is a 5 × 4 rectangle
Area = 20, the same at every depth.