Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 43 Page 424

Recall the classification of quadrilaterals. You can begin by finding the slopes of the sides.

Isosceles trapezoid

Practice makes perfect

Let's plot the given points on a coordinate plane and graph the quadrilateral.

Let's now determine the most precise name for our quadrilateral.

Name

To determine the most precise name for our quadrilateral, let's review the classification of quadrilaterals.

Quadrilateral Definition
Parallelogram Both pairs of opposite sides are parallel
Rhombus Parallelogram with four congruent sides
Rectangle Parallelogram with four right angles
Square Parallelogram with four congruent sides and four right angles
Trapezoid Quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid Trapezoid with legs that are congruent
Kite Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent

Now, let's find the slopes of the sides using the Slope Formula.

Side Slope Formula Simplified
Slope of HA: ( - 9,10), ( 2,10) 10- 10/2-( - 9) 0
Slope of AT: ( 2,10), ( 4, 4) 4- 10/4- 2 - 3
Slope of TW: ( 4, 4), ( - 11, 4) 4- 4/-11- 4 0
Slope of WH: ( - 11, 4), ( - 9,10) 10- 4/- 9-( - 11) 3

We can tell that the quadrilateral has exactly one pair of parallel sides. Therefore, it is either a trapezoid or an isosceles trapezoid. To check, we can find the lengths of the legs of the trapezoid using the Distance Formula.

Side Distance Formula Simplified
Length of AT: ( 2,10), ( 4, 4) sqrt(( 4- 2)^2+( 4- 10)^2) sqrt(40)
Length of WH: ( - 11, 4), ( - 9,10) sqrt(( - 9-( - 11))^2+( 10- 4)^2) sqrt(40)

The legs of our trapezoid are congruent. Therefore, the most precise name for this quadrilateral is an isosceles trapezoid.