Quadrilaterals and Polygons flashcards

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What is the sum of the interior angles of an n-sided polygon?Polygon Angle Sums: Break an n-sided polygon into triangles from one corner. There are n−2 triangles, each adding 180°.
What is the sum of the exterior angles of any convex polygon?Polygon Angle Sums: Walk once around the outside of any polygon. All your turns together make one full 360° turn.
How do you find one interior angle of a regular polygon?Polygon Angle Sums: A regular polygon shares its total angle sum equally among all its corners.
What is true about the opposite sides and angles of a parallelogram?Parallelograms: A parallelogram has two pairs of opposite sides that run in the same directions. Opposite sides and corners match.
How do the diagonals of a parallelogram behave?Parallelograms: Draw both diagonals. They cross halfway along each other, like two sticks balanced at their middles.
How can you prove a quadrilateral is a parallelogram?Parallelograms: To prove a shape is a parallelogram, show a property that forces both opposite sides to run parallel; do not judge by its sketch.
What are the key properties of a rectangle?Rectangles, Rhombi, and Squares: A rectangle has four square corners. Its two corner-to-corner diagonals are the same length.
What are the key properties of a rhombus?Rectangles, Rhombi, and Squares: A rhombus has four equal sides. Its diagonals cross at right angles.
What makes a quadrilateral a square?Rectangles, Rhombi, and Squares: A square passes both tests: four equal sides and four right angles.
Where is the midsegment of a trapezoid, and how long is it?Trapezoids and Kites: The trapezoid midsegment lies halfway between its parallel bases. Its length is the average of their lengths.
What is true about an isosceles trapezoid?Trapezoids and Kites: In an isosceles trapezoid, the nonparallel legs match, as do the corners along either base.
What are the key properties of a kite?Trapezoids and Kites: A kite has two pairs of neighboring equal sides. Its diagonals cross at a right angle, and one cuts the other in half.
How are the quadrilateral families related to each other?Classifying Quadrilaterals: Think of quadrilateral families as nested groups: every square also belongs to the rectangle, rhombus, and parallelogram groups.
How do you classify a quadrilateral on the coordinate plane?Classifying Quadrilaterals: Plot the four corners. Slopes tell which sides are parallel or perpendicular; distances tell which sides are equal.
What should you rely on when classifying a quadrilateral?Classifying Quadrilaterals: Use facts you can show—equal sides, right angles, parallel sides—not how a drawing happens to look.