Name: _ Date: _ Period: _
8.4 Rectangles
Rectangle: _
Properties of Rectangles
* Opposite sides are congruent and parallel
* Opposite angles are congruent (right angles)
* Consecutive angles are supplementary
* Diagonals are congruent and bisect each othe
Name: _ Date: _ Period: _
8.5 Rhombi and Squares
Rhombus: _
_
* The diagonals of a rhombus are perpendicular
* Each diagonal of a rhombus bisects a pair of opposite angles
Square: _
_
* A square has all of the properties of a rectangle and a rhombus
Examp
Name: _ Date: _ Period: _
Geometry: Chapter 7 Review
Find the geometric mean between each set of measures. Write your answer as a simplified radical.
1. 10 and 50
2.
45 and
80
Find the value of each variable. Write your answer as a simplified radical.
3.
Name: _ Date: _ Period: _
8.1 Angles of Polygons
Recall: A polygon is a closed figure with a finite number of sides. (quadrilateral, pentagon, etc)
A polygon is regular if all angles have the same measure and all sides have the same measure.
Diagonal: _
_
Name: _ Date: _ Period: _
8.2 Parallelograms
In the figure below, AB P CD and AD P BC . Name all pairs of angles for each type listed.
1. Consecutive Interior
2. Alternate Interior
3. Corresponding
4. Alternate Exterior
Parallelogram: _
Notation: Y ABCD
P
Name: _ Date: _ Period: _
8.3 Tests for Parallelograms
To determine whether a quadrilateral is a parallelogram, you must know one of the following
* Both pairs of opposite sides are parallel.
* Both pairs of opposite sides are congruent.
* Both pairs of o
Name: _ Date: _ Period: _
7.3 Special Right Triangles
!
Theorem: In a 45 45 90 triangle, the length of the
o
o
hypotenuse is
o
2 times the length of a leg.
Theorem: In a 30o 60o 90o triangle, the length of the hypotenuse is twice the
length of the shorter
Name: _ Date: _ Period: _
7.4 Trigonometry
Trigonometry: _
* trigon - triangle
* metron - measure
Trigonometric Ratio: _
Sine
sin A =
opposite
hypotenuse
Cosine
cos A =
adjacent
hypotenuse
Tangent
tan A =
opposite
adjacent
Examples: Use ABC to find each v
Name: _ Date: _ Period: _
7.5 Angles of Elevation & Depression
Angle of Elevation: _
_
Angle of Depression: _
_
Examples:
1. Find the angle of elevation of the sun when a 7.6-meter flagpole casts a 18.2 meter shadow.
2. A salvage ship uses sonar to determ
Name: _ Date: _ Period: _
7.6 The Law of Sines
sin A sin B sin C
=
=
a
b
c
*Works for any type of triangle - not just right
triangles
Law of Sines:
Examples: Find each measure using the given measures for XYZ .
1. Find x if y = 12.1 , mX = 57 , and mZ = 7
Name: _ Date: _ Period: _
7.7 The Law of Cosines
Law of Cosines
a 2 = b 2 + c 2 2bc cos A
* Works for any triangle - not just right
triangles
Examples: In BDC , given the following measures, find the measure of the missing side.
1. c = 2 , d = 5 , mB = 45