Chapter 7: Quadrilaterals and Other Polygons Flashcards

Flashcards based on lecture notes for Chapter 7, covering quadrilaterals, parallelograms, rhombuses, rectangles, squares, trapezoids, and kites.

What is a parallelogram?

A quadrilateral in which both pairs of opposite sides are parallel.

What is a rhombus?

A parallelogram with four congruent sides.

What is a rectangle?

A parallelogram with four right angles.

What is a square?

A parallelogram with four congruent sides and four right angles.

What is a trapezoid?

A quadrilateral with exactly one pair of parallel sides.

What are the bases of a trapezoid?

The parallel sides of a trapezoid.

What are the base angles of a trapezoid?

Two consecutive angles whose common side is a base.

What are the legs of a trapezoid?

The nonparallel sides of a trapezoid.

What is an isosceles trapezoid?

A trapezoid with congruent legs.

What is the midsegment of a trapezoid?

The segment that connects the midpoints of its legs.

What is a kite?

A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

What is a diagonal of a polygon?

A segment that joins two nonconsecutive vertices.

What is an equilateral polygon?

A polygon in which all sides are congruent.

What is an equiangular polygon?

A polygon in which all angles are congruent.

What is a regular polygon?

A convex polygon that is both equilateral and equiangular.

What does Corollary 7.1 state?

The sum of the measures of the interior angles of a quadrilateral is 360°.

What does Corollary 7.2, Rhombus Corollary, state?

A quadrilateral is a rhombus if and only if it has four congruent sides.

What does Corollary 7.3, Rectangle Corollary, state?

A quadrilateral is a rectangle if and only if it has four right angles.

What does Corollary 7.4, Square Corollary, state?

A quadrilateral is a square if and only if it is a rhombus and a rectangle.

What does Theorem 7.1, Polygon Interior Angles Theorem, state?

The sum of the measures of the interior angles of a convex n-gon is (n − 2) ⋅ 180°.

What does Theorem 7.2, Polygon Exterior Angles Theorem, state?

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°.

What does Theorem 7.3, Parallelogram Opposite Sides Theorem, state?

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

What does Theorem 7.4, Parallelogram Opposite Angles Theorem, state?

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

What does Theorem 7.5, Parallelogram Consecutive Angles Theorem, state?

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

What does Theorem 7.6, Parallelogram Diagonals Theorem, state?

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

What does Theorem 7.7, Parallelogram Opposite Sides Converse, state?

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

What does Theorem 7.8, Parallelogram Opposite Angles Converse, state?

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

What does Theorem 7.9, Opposite Sides Parallel and Congruent Theorem, state?

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.

What does Theorem 7.10, Parallelogram Diagonals Converse, state?

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

What does Theorem 7.11, Rhombus Diagonals Theorem, state?

A parallelogram is a rhombus if and only if its diagonals are perpendicular.

What does Theorem 7.12, Rhombus Opposite Angles Theorem, state?

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

What does Theorem 7.13, Rectangle Diagonals Theorem, state?

A parallelogram is a rectangle if and only if its diagonals are congruent.

What does Theorem 7.14, Isosceles Trapezoid Base Angles Theorem, state?

If a trapezoid is isosceles, then each pair of base angles is congruent.

What does Theorem 7.15, Isosceles Trapezoid Base Angles Converse, state?

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

What does Theorem 7.16, Isosceles Trapezoid Diagonals Theorem, state?

A trapezoid is isosceles if and only if its diagonals are congruent.

What does Theorem 7.17, Trapezoid Midsegment Theorem, state?

The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.

What does Theorem 7.18, Kite Diagonals Theorem, state?

If a quadrilateral is a kite, then its diagonals are perpendicular.

What does Theorem 7.19, Kite Opposite Angles Theorem, state?

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

Name 5 ways to prove that a Quadrilateral is a Parallelogram

1. Show that both pairs of opposite sides are parallel. 2. Show that both pairs of opposite sides are congruent. 3. Show that both pairs of opposite angles are congruent. 4. Show that one pair of opposite sides are congruent and parallel. 5. Show that the diagonals bisect each other.