Quadrilaterals: 25 flashcards
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1. What is a quadrilateral?
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A quadrilateral is a polygon with four sides, four vertices, and four angles.
2. What is the sum of the interior angles of a quadrilateral?
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The sum of the interior angles of any quadrilateral is $360^\circ$.
3. What is a diagonal of a quadrilateral?
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A diagonal is a line segment joining two non-adjacent vertices of the quadrilateral.
4. What is a regular polygon?
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A regular polygon is a polygon that is both equilateral (all sides equal) and equiangular (all angles equal).
5. What is the sum of the exterior angles of any convex polygon?
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The sum of the exterior angles of any convex polygon is $360^\circ$.
6. What is the measure of each exterior angle of a regular polygon with $n$ sides?
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Each exterior angle of a regular $n$-sided polygon is $\frac{360^\circ}{n}$.
7. What is the measure of each interior angle of a regular polygon with $n$ sides?
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Each interior angle of a regular $n$-sided polygon is $\frac{(n-2)\times 180^\circ}{n}$.
8. What is a parallelogram?
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A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
9. In a parallelogram, what is true about opposite sides?
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In a parallelogram, opposite sides are equal in length.
10. In a parallelogram, what is true about opposite angles?
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In a parallelogram, opposite angles are equal.
11. In a parallelogram, what is true about adjacent angles?
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In a parallelogram, adjacent angles are supplementary (they add up to $180^\circ$).
12. What is true about the diagonals of a parallelogram?
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The diagonals of a parallelogram bisect each other.
13. What is a rhombus?
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A rhombus is a parallelogram with all four sides equal.
14. What is true about the diagonals of a rhombus?
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The diagonals of a rhombus bisect each other at right angles ($90^\circ$).
15. What is a rectangle?
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A rectangle is a parallelogram with all four angles equal to $90^\circ$.
16. What is true about the diagonals of a rectangle?
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The diagonals of a rectangle are equal in length and bisect each other.
17. What is a square?
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A square is a parallelogram with all sides equal and all angles equal to $90^\circ$.
18. What is true about the diagonals of a square?
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The diagonals of a square are equal, bisect each other, and are perpendicular.
19. What is a kite?
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A kite is a quadrilateral with two distinct pairs of adjacent sides equal.
20. What is true about the diagonals of a kite?
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The diagonals of a kite are perpendicular, and one diagonal bisects the other.
21. What is a trapezium?
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A trapezium is a quadrilateral with at least one pair of parallel sides.
22. In an isosceles trapezium, what is true about the non-parallel sides?
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In an isosceles trapezium, the non-parallel sides (legs) are equal in length.
23. In an isosceles trapezium, what is true about the base angles?
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In an isosceles trapezium, the base angles are equal.
24. What is the angle sum property of a quadrilateral?
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The sum of the measures of the four interior angles of a quadrilateral is $360^\circ$.
25. How can you find the number of sides of a regular polygon if each exterior angle is known?
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Number of sides $n = \frac{360^\circ}{\text{each exterior angle}}$.
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