GEOMETRY FINAL HOT TIPS READ READ READ

What You Need To Be Able To Do

Obviously you NEED TO KNOW 45-45-90 AND 30-60-90. GOOGLE IT

You need to know SLOPE FORMULA and DISTANCE (just pyth. Thm - SCROLL DOWN FOR PICTURE)

The Interior Angles in A Polygon Add Up To:           (sum of interior angles)

  180(n-2)       

    i.e. hexagon = 180 x 4

Same Side Interior Angles are Supplementary      if you forget - remember the S's!!!

Triangle Congruence – 5 ways to prove

-         SSS all sides SAME

-         SAS, ASA, AAS, HL (hypotenuse and leg in right triangle are same)

Triangle Similarity – 3 ways to prove

-         SSS all sides PROPORTIONAL

-         AA – minimum 2 angles same (so ASA would be redundant)

-         SAS – two sides PROPORTIONAL and ANGLE IN BETWEEN SAME

Similarity

-         Similar things have all the same angles

-         Sides are proportional

Quadrilaterals

-         Rhombus: diagonals bisect each other and make 4 congruent triangles

-         Know what parallelograms have

-         Be able to find area of rhombus from side/diagonal lengths

Ratios of Similarity

-         1, 2, and 3 dimensions   (weight is considered a volume)

-         i.e. if the height/lengths multiplies by 8, 
then the area would multiply by 64, 
volume/weight multiplies by 8*8*8=512

Know When a triangle is impossible – two smallest sides combined must be bigger than the biggest side
IF YOU FORGET HOW THIS WORKS, VISUALIZE THIS EXAMPLE:   a triangle with lengths 1, 2, and 100 is impossible
i.e. a triangle with lengths 1, 2, and 100 is impossible
a triangle with 50,50,100 is also impossible (it would have to just be a line)

Basic HOW PROOFS WORK!!! Statements and Reasons (Two-Column)

How to Find Surface Area – add up all the areas of the sides

SOH CAH TOA

Any angle made by intersecting chords, if it is not a central angle, can be found by taking the average of the two intercepted arcs.
In picture below x = (170+70) / 2

Geometry: Final Review Questions and Answer Key

Can be downloaded here.

(Answer key is at the end.)

Chapter 10 Review

Some Vocab to know:

Inscribed angles – are half of central angle and half of their intercepted arcs

Chords intersecting in a circle: products (multiplying) of segments are equal

Central angles – 360/n

Tangent lines intersect a circle in one place only

If a tangent meets a radius/diameter they will be perpendicular.

Something is inscribed if it is inside

Something outside is “circumscribing”

Any angle made by intersecting chords, if not a central angle, can be found by taking the average of the two intercepted arcs. In picture below x = (170+70)/2

Median: go from vertex to middle of opp. Side
intersect @ CENTROID – 2:1 ratio going on inside

Perpendicular bisector: Perpendicular and goes through middle
intersect @ CIRCUMCENTER – center of circle outside triangle

Angle bisectors: lines that cut angle in half
intersect @ INCENTER – center of inside triangle

Altitude – perpendicular to opposite corner: HEIGHT
(intersect in orthocenter but don’t need to know)

Chapter 9 Test Review

A lot of content from Chapter 9 is building on content from Chapter 8.

Practice Test problems for Sections I and II here: https://dl.dropbox.com/u/40810525/chapter9practice.pdf

Chapter 9 Test:

I. Ratios of Similarity in 3 Dimensions

II. Two formulas for volume

• Prisms and Cylinders Volume = (area of base)(height)
• Pyramids and Cones Volume = (1/3)(area of base)(height)
• In chapter 8 we learned that area of the base, if it is a POLYGON the formula for area is (1/2)nsa

III. Inscribed Angle Theorem

• Practice Problems and Answer Key here: 

http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/11-Inscribed%20Angles.pdf

Geometry: Chapter 9

For Friday's Quiz there are two formulas you need to know.

Prisms and Cylinders
Have two congruent bases
V = (area of base)(height)

Pyramids and Cones
Have one base and come to a point on top
V = (1/3)(area of base)(height)

The bases can be: Circles, squares, rectangles, or polygons

If it is a polygon you treat that part like a Chapter 8 question.
Remember that area of a polygon = (1/2)*n*s*a

Imagine an ice cream cone sitting inside of a can. If their "base" was the same size, this means that the cone's volume would be (1/3) of the volume of the can of soup (cylinder).

The two worksheets WITH ANSWER KEYS can be found here:

http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/10-Volume%20of%20Prisms%20and%20Cylinders.pdf

http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/10-Volume%20of%20Pyramids%20and%20Cones.pdf

Geometry: Chapter 8 Test Review

Chapter 8
Cumulative Study Guide

Part I: Interior and Exterior Angles
Review document we made on Monday 3/11
Original Worksheet Ms. Liefland made With lots of Practice Questions

Part II: Area of Polygons
Review document we made on Tuesday 3/12
Original Worksheet Ms. Liefland made that Walks you Through the Steps

Part III: Ratios of Similarity and Circles
Original Review Sheet Ms. Liefland made
Good Video on Ratios:

Circles Summary:

HW PACKET DUE FRIDAY- DAY OF TEST
Show me your Bonus Question answer to get it circled and signed before you turn in
Monday 9-8, 9, 10, 21, ((19 BONUS))
Tuesday 9-26, 27, 28 ((BONUS))
Wednesday 9-22, 24, 40
Thursday: Board Questions and 9-41, ((72, 81 BONUS))

Algebra 2/Trig: 2/18 thru 2/22

Wednesday
Received Study Guide in Class - Combinations, Permutations, and Probability

Thursday
Review for Quiz and better probability questions (book questions are confusing)

Friday
Permutations & Probability QUiz