Geometry Final

What do you use to find similar triangles

Big Triangle=Lil Triangle

when a problem says prove (for ex.) AD/DE=AB/BC

use corresponding sides of similar triangles are congruent (CPCTC)

when you use distance

segments are congruent, answers will be equal

1. when you use slope

to show segments are parallel, answers will be equal

legs in party hat are

congruent

2. when you use slope

segments are perpendicular or right angle, answers will be opposite reciprocals

intersecting chords are

equal to each other

how to prove triangles are congruent

SAS,SSS,AAS,ASA,HL

wex=wex

whole exterior= whole exterior

when you use midpoint

to prove segment bisect each other, answers will be equal

slope intercept formula

y=mx+b

slope formula

y2-y1/x2-x1

point slope formula

y-y1=m(x-x1)

translation

slide

when a problem says prove (for ex) RP•OQ=MO•OP

use product of the means = product of the extremes

distance formula

d=(x2-x1)+(y2-y1) UNDER SQUARE ROOT

slope formula

y2-y1/x2-x1

midpoint formula

M= (x1+x2/2 , y1+y2/2)

45-45-90

1,1, square root 2 (hypotenuse), then cross multiply

30-60-90

1 (at shortest side), 2 (at hypotenuse), square root 3 (on last side), then cross multiply

heartbeat

seg 1/alt = alt/seg 2

HLLS

Hypotenuse/ leg 1= leg 2/ segment

SOH CAH TOA

sine, cos, tan

equation of a circle

(x-h)2+(y-k)2=r2, (h,k) is the center r is radius

how to find the sum of interior angles

(h-2)180

how to find sum of exterior angles

divide 360 by number of sides

area of trapezoid

a=1/2 (b1+b2) h

inscribed angle

vertex is on the circle, ½ (arc)

when you have intersecting chords in a circle

angle=arc+arc/2

when you have what looks like a supplementary angle in a circle

1/2(arc of the angle you’re looking for)

rotation

turn, positive=counterclockwise negative= clockwise

reflection

flip, switch x and y and change the signs

dilation

to make bigger

scale factor

for ex. k=2, multiply x and y by 2

rotational symmetry

when figure looks the same after a turn greater than or equal to 360

order

number of times a figure can be rotated and look the same

magnitude

amount of degrees a figure can be rotated and look the same

central angle

equal to its arc

How to prove Simular triangles

AA, SSS, SAS

Use slope for a rhombus When…

Diagonals are perpendicular

Use distance for a rhombus when

There are four congruent sides

Use slope in a rectangle when proving

All angles equal 90°

Use distance in a rectangle when proving

Diagonals are congruent

Use distance in a parallelogram when proving

Two pairs of opposite sides are congruent

Use slope in a parallelogram when proving

Two pairs of opposite sides are parallel

Use midpoint in a parallelogram

When trying to prove diagonals bisect each other

Rules for parallelogram

Parallel sides, opposite sides are congruent, diagonals bisect, consecutive angles are supplementary opposite angles are congruent

Rules for rectangle

Four right angles diagonals are congruent

Rules for rhombus

four congruent sides, diagonals bisect angles diagonals are perpendicular

Rules for square

All sides are congruent diagonals are perpendicular angles equal 90°

Rules for trapezoid

One pair of parallel lines, consecutive angles are supplementary

Isosceles trapezoid rules

Base angles are congruent diagonals are congruent Legs are congruent

how to find measure of exterior angle in a circle

exterior angle=big arc-lil arc/2