gemometry final

how to solve rations

make a proportion then cross multiply

perimeters of similar polygons

the perimeter ratio equals scale factor

area of similar polygons

the area ratio equals the scale factor squared

Similarity theorems

AA

SSS- if all sides are proportional

SAS

Triangle proportionality theorem

If a line parallel to one side of a triangle intersects the other two sides then it divides the two sides proportionatly

Three parallel lines theorem

If 3 parallel lines intersect 2 tranversals they divide proportionalty

Triangle angle bisector theorem

If a ray bisects a triangle angle then it segments are proportional to the sides

Triangle midsegment

half the 3rd side

classifing a triangle

Right- sum and product is same

Acute- sum is greater than product

Obtuse- sum is less than product

Right triangle similarity theorem

If a big triangle is split by a altitude then the 2 triangles are similar

Area of triangle (sin)

Area = 1/2(bc) Sin A

Law of Sines

Sin A / a = Sin B / b = Sin C / c

Law of Cosines

a² = b² + c² - 2bc cos A

Sum of polygon interior angles

(n-2) x 180

sum of polygon exterior angles

360

parallelogram characteristics

opposite sides congruent

opposite angles congruent

consecutive angles supplementary

diagonals bisect

Rhombus Characteristics

Diagonals perpendicular and bisect angles

Congruent sides

Rectangle characteristics

diaganols congruent

4 right angles

kite characteristics

2 pairs of congruent sides

1 pair of congruent angles

diaganols perpendicular

Trapazoid

1 pair of parallel sides

isoceles trapezoid characteristics

congruent legs

congruent base angles

congruent diaganols

trapezoid midsegment

half the sum of the bases

tangent radius relationaship

tangent is perpendicular to radius

external tangent congruence theorem

tangents from a common external point are congruent

measure of minor arc

central angle

Ways minor arcs are congruent

central angles congruent

congruent chords

perpendicular chord bisector theorem

if diameter bisects a chord then it bisects the chord and arc

equidistant chords theorem

2 chords are congruent if they are equidistant

inscribed angle

inscribed angle is half the arc

inscribed quadrilateral

opposite angles are supplementary

Tangent and intersected chords theorem

If a tangent and chord intersect then each angle made is half the intercepted arc

Angles inside a circle

if 2 chords intersect inside a circle then the angle is half sum the intercepted verticle arcs

If 2 tangents or secants intersect (angles)

The angle is half the DIFFERENCE of the intercepted angles

The angle is 180 minus the central angle that interceptes the same arc

Segments of chords (inside circle)

If 2 chords intersect the products of the segments are equal

If 2 secants join outside a circle

whole secant x external secant = whole secant x external secant

If a tangent and secant join outside the circle (segments)

the tangent squared = the external x whole secant