Geometry Chapter 6 Flashcards

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Questions and Answers

What is a parallelogram?

A quadrilateral with at least one pair of parallel sides

A quadrilateral with all sides equal

A quadrilateral with both pairs of opposite sides parallel (correct)

A quadrilateral with four right angles

What is a rhombus?

A parallelogram with 4 congruent sides

What defines a rectangle?

A parallelogram with 4 right angles

What is a square?

A parallelogram with 4 congruent sides and 4 right angles Signup and view all the answers

What is a kite in geometry?

A quadrilateral with two pairs of adjacent sides congruent and no opposite angles congruent Signup and view all the answers

What is a trapezoid?

A quadrilateral with exactly one pair of parallel sides Signup and view all the answers

What is an isosceles trapezoid?

A trapezoid whose nonparallel sides are congruent Signup and view all the answers

State Theorem 6-1 regarding the sides of a parallelogram.

Opposite sides of a parallelogram are congruent Signup and view all the answers

What are consecutive angles in a polygon?

Angles of a polygon that share a side Signup and view all the answers

State Theorem 6-2 regarding the angles of a parallelogram.

Opposite angles of a parallelogram are congruent Signup and view all the answers

State Theorem 6-3 regarding the diagonals of a parallelogram.

The diagonals of a parallelogram bisect each other Signup and view all the answers

State Theorem 6-5 regarding congruent opposite sides.

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Signup and view all the answers

State Theorem 6-6 regarding congruent opposite angles.

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Signup and view all the answers

State Theorem 6-7 regarding the bisecting diagonals.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Signup and view all the answers

State Theorem 6-8 regarding congruent and parallel sides.

If one pair of opposite sides is both congruent and parallel, then the quadrilateral is a parallelogram Signup and view all the answers

State Theorem 6-9 regarding the diagonal-angle of a rhombus.

Each diagonal of a rhombus bisects two angles of the rhombus Signup and view all the answers

State Theorem 6-10 regarding the diagonals of a rhombus.

The diagonals of a rhombus are perpendicular Signup and view all the answers

State Theorem 6-11 regarding diagonals of a rectangle.

The diagonals of a rectangle are congruent Signup and view all the answers

State Theorem 6-12 related to a parallelogram.

If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus Signup and view all the answers

State Theorem 6-13 regarding perpendicular diagonals.

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus Signup and view all the answers

State Theorem 6-14 regarding congruent diagonals.

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle Signup and view all the answers

What are the bases of a trapezoid?

The parallel sides Signup and view all the answers

What are the legs of a trapezoid?

Nonparallel sides Signup and view all the answers

What are the base angles of a trapezoid?

The two angles that share a base Signup and view all the answers

State Theorem 6-15 regarding base angles of an isosceles trapezoid.

The base angles of an isosceles trapezoid are congruent Signup and view all the answers

What can be said about angles that share a leg in a trapezoid?

The bases of a trapezoid are parallel. Therefore, the two angles that share a leg are supplementary Signup and view all the answers

State Theorem 6-16 regarding the diagonals of an isosceles trapezoid.

The diagonals of an isosceles trapezoid are congruent Signup and view all the answers

State Theorem 6-17 regarding the diagonals of a kite.

The diagonals of a kite are perpendicular Signup and view all the answers

What is the midsegment of a trapezoid?

The segment that joins the midpoints of the nonparallel opposite sides Signup and view all the answers

State Theorem 6-18 regarding the trapezoid midsegment.

<ol> <li>The midsegment of a trapezoid is parallel to the bases. 2. The length of the midsegment of a trapezoid is half the sum of the lengths of the bases.</li> </ol> Signup and view all the answers

Study Notes

Types of Quadrilaterals

Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Rhombus: A type of parallelogram characterized by having four congruent sides.
Rectangle: This parallelogram has four right angles.
Square: A special parallelogram with both four congruent sides and four right angles.
Kite: Defined as a quadrilateral with two pairs of adjacent sides that are congruent, but no opposite angles are congruent.
Trapezoid: A quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid: A trapezoid where the nonparallel sides are congruent.

Theorem 6-1: Opposite sides of a parallelogram are congruent.
Theorem 6-2: Opposite angles of a parallelogram are congruent.
Theorem 6-3: The diagonals of a parallelogram bisect each other.
Theorem 6-5: A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.
Theorem 6-6: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
Theorem 6-7: A quadrilateral is a parallelogram if the diagonals bisect each other.
Theorem 6-8: A quadrilateral is a parallelogram if one pair of opposite sides is both congruent and parallel.

Special Properties of Rhombuses and Rectangles

Theorem 6-9: Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 6-10: The diagonals of a rhombus are perpendicular.
Theorem 6-11: The diagonals of a rectangle are congruent.
Theorem 6-12: If one diagonal of a parallelogram bisects two angles, the parallelogram is a rhombus.
Theorem 6-13: A parallelogram with perpendicular diagonals is a rhombus.
Theorem 6-14: A parallelogram with congruent diagonals is a rectangle.

Trapezoid Properties and Theorems

Bases: The parallel sides of a trapezoid.
Legs: The nonparallel sides of a trapezoid.
Base Angles: Two angles that share a base in a trapezoid.
Theorem 6-15: Base angles of an isosceles trapezoid are congruent.
Angles that Share a Leg: These angles are supplementary due to the parallel bases of the trapezoid.
Theorem 6-16: The diagonals of an isosceles trapezoid are congruent.
Theorem 6-17: The diagonals of a kite are perpendicular.

Coordinate Plane Conventions

Place the vertex of figures at the origin, with one side along an axis, or center the figure around the origin for convenience in calculations.
Midsegment of a Trapezoid: The segment connecting the midpoints of the nonparallel sides.
Theorem 6-18:
- The midsegment of a trapezoid is parallel to the bases.
- The length of the midsegment is half the sum of the lengths of the bases.

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Description

Test your knowledge of key terms in geometry with these flashcards from Chapter 6. This quiz covers various types of quadrilaterals and their properties, including parallelograms, rhombuses, rectangles, squares, and kites. Perfect for students looking to reinforce their understanding of geometric shapes!