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GRE Math: Quadrilaterals And Other Polygons

Subjects : gre, math

Instructions:

Answer 10 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. trapezoid
(n-2)180
360
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
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. polygons: sum of all exterior angles
360
(n*(n-3)/2 where n>=3
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

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

4. kite
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)
360
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
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

5. polygons: number of diagonals is
(n*(n-3)/2 where n>=3
quadrilateral with parallel opposite sides
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

6. square
(n*(n-3)/2 where n>=3
quadrilateral with parallel opposite sides
360
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2

7. polygons: sum of all interior angles
(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
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
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2

8. rhombus
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
Opposite angles are equal - consecutive angles are supplementary - opposite sides are equal - diagonals bisect each other - area= b*h - perimenter = 2b + 2c
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

9. rectangle
(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
Parallelograms with right angles - all angles are 90 - diagonals are equal (not perpendicular) - perimeter = 2b+2a - area = a*b
(n*(n-3)/2 where n>=3

10. parallelogram
All sides are equal - all angles are 90 - both diagonals bisect each other at 90 - each diagonal is ssqrt2 - area = s^2
360
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