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)