Geometry

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MAT.126 4.4

por David Kedrowski

Chapter 5: Trigonometric Function

por Yap Wei Li

Triangle properties

por Leah Irmiter

Grade 10 Mathematics

por Kiana Roomes

Geometry

Circles

If 2 tangent segments to a circle share a common endpoint outside the circle, then the 2 segments are congruent.

If a line in plane of a circle is perpendicular to a radius at the endpoint to a circle.

If a line is tangent to a circle, the line is perpendicular to the radius @ the point of tangency.

circles in the coordinate plane : (x-h) squared + (y-k) squared = r squared

(p+q)p=tsquared

(w+x)w=(y+2)y

segment lengths --- a*b=c*d

circumference

radius

locus

tangent to a circle

point of tangency

arcs

intercepted arc

Secants

Chords

Proofs

2 column

flow

paragraph

triangles

Pythagorean Theorem- If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

HL

Triangle sum theorem

SAS

SSS

AA~

AAS

Surface Area=LA + 2B

Lat. Area=1/2PBl

area=1/2bh

volume= 1/3bh

equilateral triangles

acute triangles

If the square of the length of the longer side of a triangle is greater than the sum of the other two sides then the triangle is acute.

obtuse triangles

If the square of the length of the side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

Right triangles

45-45-90 triangles

In a 45-45-90 triangle both legs are congruent and the length of the hypotenuse is square root of 2 times the length of the leg

scalene triangles

30-60-90 triangles

In a 30-60-90 triangle the length of the hypotenuse is twice the length of the shorter leg. the length of the longer leg is square root of 3 times the length of the shorter leg.

isosceles

Volume

cones

rectangular prisms

bwh

spheres

4/3(pi)r3

pyramids

1/3bh

cylinders

(pi)r2h

similar solids have a ratio of a3:b3

V-bwh

Area

The length of an arc of a circle is the product of the ratio measure of arc/360 and the circumference of the circle.

A=1/2ap

A=bh

C=2(pi)r

C=(pi)d

A=1/2h(b1 +b2)

A=1/2b2(sinA)

A= 1/2 bh

A=1/2 d1d2

arc length

segment of a circle

central adjacemt arcs

apothem

concentric circle

congruent arcs

diameter

sector of circle

Trigonometry

45,45,90=x:x:2x

cosine

adjacent____hypotenuse

tangent

opposite____adjacent

sine

opposite___hypotenuse

Congruency

If a transversal intersents two parallel lines, then alternate interior and alternate exterior angles are congruent

If a transversal intersects two parallel lines, then corresponding angles are congruent.

All right angles are congruent

If 2 angles are supplements/compliments of the same angle (or 2 congruent angles)then the 2 angles are congruent

SAS,ASA,AAS,SSS,CPCIP

Vertical angless are congruent

Angles

M

Perpendicular Lines form right triangles

Acute

Obtuse

alternate interior angles are =

Same Side Interior Angles

Corresponding Angles Postulate

Alternate Exterior Angles

parallel lines

skew lines

Angle Measures

~=angles

Angles in transversals

Adjacent

Supplementary

Right

Vertical

Complementary

Conditional Statements

~q-->~p

~p-->~q

q-->p

p-->q

law if detachment

law of syllogism

biconditional

conditional

inverse

negation

counterexample

contrapositive

converse

theorem

deductive reasoning

inductive reasoning

Polygons (regular)

6-11

6-5

6-3

6-4

6-22

6-15

6-7

6-12

6-13

6-8

6-21

consecutive angles

parrallelogram

diagonals are congruent

4 right angles

rhombus

diagonals are perpendicular

4 congruent sides

diagonals bisect

polygon

equilateral/equiangular

base angle

square

leg of a trapezoid

rectangle

coordinate proof

opposite angle

kite

quadrilateral with 2 pairs of consecutive sides congruent and no opposite sides are congruent

regular polygon

base

trapezoid

exactly 1 pair of parallel sides (bases)

midsegment of a trapezoid

oppostie sides

isoscles trapezoid

2 sides that are congruent and a pair of angles that are congruent

Transformations

A translation or rotation is a compostion of two reflections

There are only 4 isometry

dialation

enlargement

reduction

center

scale factor

scale factor translations

pre-images

tessellation

isometry

point/line/rotation/reflectional symmetry

line of reflection

reflections

symmetry

reflectional symmetry

line symmetry

point symmetry

angle rotation

translational symmetry

center of a regular polygon

rotations

translation made of 2 reflections

Parallelograms

Opp. Sides ~=

Diagonals bisect Opp

Consecutive angles supp.

Opposite Sides

Opposite Angles

Consecutive Angles