# Geometry Review

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1. 6.1 Basic Geometric figures
1) Segment
2) Ray
3) Line
• 1) A segment is a geometric figure consisting of two points called endpoints.
• • 2) Ray Consists of a segment and all points between A and B and all points beyond b
•  • 3) Line Can consist of two rayes such as PQ and QP - can be named as a smaller letter m
• Lines can be coplanar - Parrallel (l||m) or they can be intersecting
• 2. 6.1 Basic Geometric Figures Angles
1) What is an Angle
2) Types of Angles
• 1) An Angle is a set of points consisting of two rays or half lines with a common end point, this end point is called a vertex
• Unit of Measure is degrees
• • 2) Types of Angles
• a) Right angle = 90 degrees
• b)Acute angle - greater than 0 and less than 90 degrees
• c)Obtuse Angle - greater than 90 and less than 180 degrees
• d) Straight angle - measure is 180 degrees
3. 6.1 Basic Geometric figures
Perpendicular Lines
• Two lines a perpendicular if they intersect to form a right angle
• 4. 6.1 basic Geometric figures - Polygons
What are polygons?
What are the most common polygons?
• 1) Polygons are shapes made up of 3 or more sides
• 5. 6.1 Basic Geometric shapes - Triangles
What is a triangle and what are the different types?
• 1) Triangles are polygons of 3 or more sides
• 2) types of triangles
• a)Equilateral Triangle - all sides same length
• b)Isosceles Triangle - two sides are the same length
• c)Scalane Triangle - All sides are of different lengths
• d) right triangle - one angle is 90 degrees
• e)Obtuse triangle - One angle is an obstuse angle between 90 and 180 degrees
• f)Acute triangle - all three angles are acute - less than 90 degrees
6. 6.1 Basic Geometric figures - sum of angle measures for polygons
1)How do you find the sum of angles for more complex polygons?
2) What is the sum of angles for all triangles?
• 1)Take the number of sides (n) subtract 2 and multiply by 180 degrees
• (n-2)*180 degrees
• 2) Sum of three angles in a triangle is 180 degrees
7. 6.2 Perimeter og a polygon
1) What is perimeter?
2) Formulas for perimeter of a square and rectangle?
• 1) A polygons is a geometric figure with three or more sides.
• The perimeter of a polygon is the distance around it or the sum of length of its sides
• 2) Perimeter of a rectangle
• P=2(l*w)
• 3) Square
• P=4*s
8. 6.3 Area of Rectangles, Squares, parallelogram, triangle and trapezoid
1) Define area
2) Formulas for areas of various polygons
• 1) Area is defined as the measure of the interior form of a plane region
• Area is expressed as squared - IE 5 sqr feet etc
• Square units
• 2) Common formulas
• Rectangle - A=l.w
• Square - A= s2
• Parellelogram - A = b*h (four sided figure with two pairs of parallel sides)
• • Triangle A= 1/2*b*h
• Trapezoid A=1/2*h*(a+b) (polygon with 4 fours, two of which are bases which are parallel to each other
• 9. 6.4 Circles - Radius, Diameter, Circumference and Area
1) Define each of Radius, Diameter and Circumference
2) Formulas for each Radius, Diameter and Circumference
• 1) Diameter - length across the circle
• Radius - length from center point to end
• Circumference - distance around the circle
• 2)
• Diamter d = 2*r
• Circumference - when radius is known
• C=2πr
• Circumference when Diameter is known
• C=πd
• Area
• A=πr2
10. 6.5 Volume and Surface Area
1) Define formulas for Rectangule solid, circular cylinder, sphere and cone
• Volume is expressed as cubic units
• 1) Rectangular Solids - Volcume is the number of unit cubes needed to fill it
• V=l*w*h
• Surface area of a rectangular solid - total area of the six rectangles that form the surface of the solid
• SA=2(lw+lh+wh)
• 2) Cylinders
• V=B*h or V=πr2 h
• • 3)Spheres
• V=4/3πr3
• 4)Cones
• V=1/3*B*h or V=1/3πr2 h
• 11. 6.6 Relationships between Angle measures
1)Define complementary and supplementary angles
• 1)Two angles are complementary when the sum of their measures is 90 degres
• Each angle is said to complement of the other
• These are said to be acute angles - when they are adjacent they form a right angle
• • 2) Supplementary angles - angles are supplementary when the sum of the measure is 180 degrees
• Each angle is called the supplement of the other
• 12. 6.6 Relationships between Angle measures - Congruency
1) define congruent angles and segments
• 1) Congruent segments - two segments that have the same length
• 2) Congruent angles - angles that have the same measure
13. 6.6 Relationships between Angle measures Vertical Angles
1) define what a vertical angle is
2)What is the vertical angle property?
• 1) two nonstraight angles are vertical angles if and only if their sides form two pairs of opposite rays
• • Angles RPQ and SPT are called veritcal angles
• 2) The vertical angle property - these angles are congruent
14. 6.6 Relationships between Angle measures - Transversals and Angles
1) Define a transversal
2) what are the angle types formed?
• 1) A transversal is a line that intersects two or more coplanar lines in different points
• When a transversal intersects a pair of lines, eight angles are formed
• 2) - Angle types formed
• Corresponding Angles - expressed in pairs
• • <2 and <6, <3 and <7, <1 and <5, <4 and <8
• Interior angles - not expressed in pairs
• • <3, <4,<5,<6
• Alternate Interior Angles - expressed as pairs
• • <4 and <6, <3 and <5
15. 6.6 Relationships between Angle measures
Properties of Parralle Lines
• 1) In a transversal intersects two parallel lines, then the corresponding angles are congruent
• • 2) If a transversal intesects two parallel lines, then the alternate interior angles are congruent
• • 3) In a plane, if two lines are parallel to a third line, then the two lines are parallel to each other
• • 4) if a tranversal intersects two parralel lines, then the interior angles on the same side
• of the transversal are supplementary
• • 5) if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
• 16. 6.7 Congruent triangles and properties of parallelograms
1) Define Triangle types
2) Define the three properties to show why triangles are congruent
• 1) Classify triangles by their angles
• Acute: All angles are acute ( less than 90 degrees)
• Right: One angle is a right angle ( 90 degrees)
• Obtuse: One obtuse angle ( greater than 90 degress less than 180 degrees
• Equiangular: all angles are congruent
• 2) Classify triangles by their sides
• Equilateral: All sides are congruent
• Isosceles - at least two sides are congruent
• Scalane - No sides are congruent

• 3) Three properties to show why triangles are congruent
• Triangles are congruent if and only if their vertices can be matched so that the corresponding angles and sides are congruent
• Corresponding sides and angles of two congruent triangles are called corresponding parts of congruent triangles
• Corresponding parts of congruent triangles are always congruent
• We write to say that are congruent
• • • The side-Angle-Side SAS property
• Two triangles are congruent if two sides and the included angle of one triangle are congruent to
• two sides and the included angle of the other triangle

• The Side-Side-Side (SSS) property
• If three sides of one triangle are congruent to three sides of another triangle
• then the triangles are congruent

• The Angle-Side-Angle (ASA) property
• If two angles and the included side of a triangle are congruent to two angles and the
• included side of another triangle , then the triangles are congruent
17. 6.7 Congruent triangles and properties of parallelograms
Define the properties of parallelograms
• 1) A diagonal of a parallelogram determines two congruent triangles
• 2) The opposite angles of a paralleogram are congruent
• 3) The opposite sides of a paralleogram are congruent
• 4) Consecutive angles of a parallelogram are suppelmentary
• 5) Diagonals of a parallelogram bisect each other
18. 6.8 Similar Triangles
Review similar triangles
• Triangles can be similar to each other but not congruent in size
• • Two triangles are similar in and only if their vertices can be matched so that their corresponding angles are congruent and the
• lengths of corresponding sides are proportional
• To say that <>ABC and <>DEF are similar we write"<>ABC ~<>DEF"
• • Thus, <>ABC ~ <>DEF means that
• Author: treborprime ID: 25558 Card Set: Geometry Review Updated: 2010-07-02 22:11:07 Tags: WGU Geometry review Folders: Description: QLC1 Geometry review Show Answers: