Exercise 114 Page 134

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

SubstituteValues

Substitute values

P(at least two sides congruent)=7/8

CalcQuot

Calculate quotient

P(at least two sides congruent)=0.875

WritePercent

Convert to percent

P(at least two sides congruent)=87.5 %

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

SubstituteValues

Substitute values

P(two pairs of parallel sides)=3/8

CalcQuot

Calculate quotient

P(two pairs of parallel sides)=0.375

WritePercent

Convert to percent

P(two pairs of parallel sides)=37.5 %

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

SubstituteValues

Substitute values

P(at least one pair of parallel sides)=5/8

CalcQuot

Calculate quotient

P(at least one pair of parallel sides)=0.625

WritePercent

Convert to percent

P(at least one pair of parallel sides)=62.5 %