a To determine probability, we divide the number of favorable outcomes with the number of possible outcomes.
B
b Note that we are looking for shapes with exactly two pairs of parallel sides.
C
c The sentence "at least one pair" includes shapes with only one pair of parallel sides.
A
a 87.5 %
B
b 37.5 %
C
c 67.5 %
Practice makes perfect
a To determine probability, we divide the number of favorable outcomes with the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomesIn the bucket, we have a total of 8 shapes. Out of these, 7 shapes have at least two sides that are congruent.
the equilateral triangle
the isosceles right triangle
the regular hexagon
the rhombus
the kite
the parallelogram
the rectangle
With this, we can calculate the probability of picking one of these shapes using the Probability Formula.
P=Number of favorable outcomes/Number of possible outcomes
b No triangles have any parallel sides and therefore, the first two shapes can be disregarded. A regular hexagon is a polygon with 6 congruent sides. Let's draw this shape.
As we can see, a regular hexagon has three pairs of parallel sides.
Any trapezoid is defined as a quadrilateral where two sides are parallel.
A rhombus is a quadrilateral with two pairs of parallel and congruent sides.
A kite is a shape with two pairs of congruent sides.
Examining the diagram, we see that it does not have any parallel sides.
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rectangle is a subset of a parallelogram with the additional requirement that its four angles are right angles.
As we can see, there is a total of three shapes with two pairs of parallel sides. With this, we can calculate the probability of picking one of these shapes.
P=Number of favorable outcomes/Number of possible outcomes
c From Part B, we know that there is at least one pair of opposite sides in the rectangle, parallelogram, rhombus, non-isosceles trapezoid, and the regular hexagon for a total of 5 shapes. With this, we can calculate the probability of picking a shape with at least one pair of parallel sides.
P=Number of favorable outcomes/Number of possible outcomes
