Download RGeo Ch 6 Study Guide

Regents Geometry
Chapter 6 Study Guide
Use the following website for on-line resources (practice tests and quizzes):
http://www.glencoe.com/sec/math/geometry/geo/geo_04/self_check_quiz/index.php/na
Select Chapter 8 Quadrilaterals or use the resources found in the left-hand toolbar.
Chapter 6 – Quadrilaterals
 Definitions with images can be found using Quizlet: http://quizlet.com/_eqtrg
Diagonal of a Polygon
A segment that connects any two non-consecutive vertices.
Sum of the Interior Angles of a Polygon For an 𝑛-sided convex polygon, the sum is equal to (n-2)*180
Sum of the Exterior Angles of a Polygon
The sum of the exterior angles of a convex polygon with
one angle at each vertex is equal to 360.
Quadrilateral A four-sided polygon.
Parallelogram A quadrilateral with both pairs of opposite sides parallel.
If a quadrilateral is a parallelogram, then...
1. Its opposite sides are congruent.
2. its opposite angles are congruent.
3. its consecutive angles are supplementary.
If a quadrilateral has one right angle, then... It has four right angles.
Diagonals of Parallelograms - 1
If a quadrilateral is a parallelogram, then its diagonals bisect
each other.
Diagonals of Parallelograms - 2
If a quadrilateral is a parallelogram, then each diagonal
separates the parallelogram into two congruent triangles.
If both pairs of opposite sides of a quadrilateral are parallel, then...
The quadrilateral is a parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then... The quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then... The quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then...
The quadrilateral is a parallelogram.
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then...
The quadrilateral is a parallelogram.
Rectangle
Properties of Rectangles
Diagonals of a Rectangle - 1
Diagonals of a Rectangle - 2
A parallelogram with four right angles.
1. All four angles are right angles.
2. Opposite sides are parallel and congruent.
3. Opposite angles are congruent.
4. Consecutive angles are supplementary.
5. Diagonals bisect each other.
6. Diagonals are congruent.
If a parallelogram is a rectangle, then its diagonals are congruent.
If the diagonals of a parallelogram are congruent, then the
parallelogram is a rectangle.
Rhombus
If a parallelogram is a rhombus, then...
Square
A parallelogram with four congruent sides.
1. Its diagonals are perpendicular.
2. Each diagonal bisects a pair of opposite angles.
A parallelogram with four congruent sides and four right angles.
A parallelogram that is both a rectangle and a rhombus.
If the diagonals of a parallelogram are perpendicular, then...
If one diagonal of a parallelogram bisects a pair of opposite angles, then...
If one pair of consecutive sides of a parallelogram are congruent, then...
If a quadrilateral is both a rectangle and a rhombus, then...
The parallelogram is a rhombus.
The parallelogram is a rhombus.
The parallelogram is a rhombus.
The quadrilateral is a square.