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GRE Math: Quadrilaterals And Other Polygons

Subjects : gre, math

Instructions:

Answer 10 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. polygons: number of diagonals is
360
Opposite angles are equal - consecutive angles are supplementary - opposite sides are equal - diagonals bisect each other - area= b*h - perimenter = 2b + 2c
(n*(n-3)/2 where n>=3
2 pairs of adjacent congruent sides - the diagonals are perpendicular to each other - the longer diagonal bisects the shorter - the longer diagoanl bisects the two angles whose vertices are its endpoints

2. parallelogram
quadrilateral with parallel opposite sides
360
quadrilateral with one pair of parallel sides - parallel sides are bases - heights are equal - legs may or may no be equal (=isosceles trapezoid) - diagonals may or may not be equal - area = .5h(b1+b2)
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2

3. rectangle
2 pairs of adjacent congruent sides - the diagonals are perpendicular to each other - the longer diagonal bisects the shorter - the longer diagoanl bisects the two angles whose vertices are its endpoints
(n*(n-3)/2 where n>=3
Equilateral parallelogram - opposite angles are equal - all sides are equal - diagonals are perpendicular to each other - perimeter=4s - area =b*h= half the product of the diagonals
Parallelograms with right angles - all angles are 90 - diagonals are equal (not perpendicular) - perimeter = 2b+2a - area = a*b

4. facts about parallelograms
(n-2)180
Opposite angles are equal - consecutive angles are supplementary - opposite sides are equal - diagonals bisect each other - area= b*h - perimenter = 2b + 2c
(n*(n-3)/2 where n>=3
360

5. trapezoid
(n*(n-3)/2 where n>=3
quadrilateral with one pair of parallel sides - parallel sides are bases - heights are equal - legs may or may no be equal (=isosceles trapezoid) - diagonals may or may not be equal - area = .5h(b1+b2)
Opposite angles are equal - consecutive angles are supplementary - opposite sides are equal - diagonals bisect each other - area= b*h - perimenter = 2b + 2c
quadrilateral with parallel opposite sides

6. polygons: sum of all interior angles
quadrilateral with one pair of parallel sides - parallel sides are bases - heights are equal - legs may or may no be equal (=isosceles trapezoid) - diagonals may or may not be equal - area = .5h(b1+b2)
2 pairs of adjacent congruent sides - the diagonals are perpendicular to each other - the longer diagonal bisects the shorter - the longer diagoanl bisects the two angles whose vertices are its endpoints
Parallelograms with right angles - all angles are 90 - diagonals are equal (not perpendicular) - perimeter = 2b+2a - area = a*b
(n-2)180

7. polygons: sum of all exterior angles
Parallelograms with right angles - all angles are 90 - diagonals are equal (not perpendicular) - perimeter = 2b+2a - area = a*b
quadrilateral with parallel opposite sides
2 pairs of adjacent congruent sides - the diagonals are perpendicular to each other - the longer diagonal bisects the shorter - the longer diagoanl bisects the two angles whose vertices are its endpoints
360

8. square
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2
Parallelograms with right angles - all angles are 90 - diagonals are equal (not perpendicular) - perimeter = 2b+2a - area = a*b
360
(n-2)180

9. kite
(n*(n-3)/2 where n>=3
2 pairs of adjacent congruent sides - the diagonals are perpendicular to each other - the longer diagonal bisects the shorter - the longer diagoanl bisects the two angles whose vertices are its endpoints
(n-2)180
quadrilateral with one pair of parallel sides - parallel sides are bases - heights are equal - legs may or may no be equal (=isosceles trapezoid) - diagonals may or may not be equal - area = .5h(b1+b2)

10. rhombus
(n-2)180
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2
(n*(n-3)/2 where n>=3
Equilateral parallelogram - opposite angles are equal - all sides are equal - diagonals are perpendicular to each other - perimeter=4s - area =b*h= half the product of the diagonals