Studied by 41 people

4.5(2)

Get a hint

Hint

1

sum of interior angles

180(number of triangles-2)

New cards

2

each interior angle of a regular polygon

180(number of triangles-2)/number of triangles

New cards

3

sum of exterior angles

360

New cards

4

each exterior angle

360/number of triangles

New cards

5

scalene triangle

no congruent sides

New cards

6

equilateral triangle

all sides are congruent

New cards

7

isosceles traingle

2 congruent sides

New cards

8

equiangular

3 congruent angles

New cards

9

exterior angle theorem

The exterior angle is equal to the sum of the two non-adjacent interior angles

New cards

10

midsegment

a segment that joins two midpoints

always parallel to the third side

1/2 the length of the 3rd side

splits the triangle into 2 similar triangles

New cards

11

slope intercept form of a line

y = mx + b, where m is the slope and b is the y-intercept.

New cards

12

point slope form of a line

**y-y1=m(x-x1).** where m is the slope and x1 and y1 are the values of a given point on the line

New cards

13

slope formula

(y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on a line. rise/run

New cards

14

parallel lines

have the same slope

New cards

15

perpendicular lines

have neg reciprocal slopes (flip the fraction and change the sign into its opposite)

New cards

16

collinear points

are points that lie of the same line

New cards

17

mid point formula

It involves averaging the x and y coordinates of the endpoints.

Formula: M =(x₁+x₂)/2, (y₁+y₂)/2.

New cards

18

distance formula

**d = √((x2 - x1)^2 + (y2 - y1)^2)**, where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them.

New cards

19

segment ratios

the ratio of the lengths of two segments that share an endpoint.

New cards

20

triangle theorems

the sum of 2 sides must be greater than the 2 sides

the difference of 2 sides must be less than the 3rd side

the longest side of the triangle is opposite the largest angle

the shortest side of the triangle is opposite the smallest angle

New cards

21

isosceles triangle properties

2 congruent sides and 2 congruent base angles

the altitude drawn from the vertex is also the median and angle bisector

if two sides of a triangle are congruent, then the angles opposite those congruent angles congruent

New cards

22

alternate interior amgles

are congruent

New cards

23

alternate exterior angles

New cards

24

corresponding angles

New cards

25

same side interior angles

supplemantary

New cards

26

side splitter theorem

if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

New cards

27

triangle congruency theorems

New cards

28

CPCTC

If two triangles are congruent, then their corresponding parts are congruent.

New cards

29

similar triangle theorems

Similar figures have congruent angles and proportional sides

CSSTP-Corresponding Sides of Similar Triangles are in Proportion

In a proportion, the product of the means equals the product of the extremes

New cards

30

altitude theorem SAAS

The altitude is the geometric mean between the 2 segments of the hypotenuse

New cards

31

leg theorem

The leg is the geometric mean between the segment it touches and the whole hypotenuse.

New cards

32

confunctions

sine and cosine are confunctions which are complemntary (add up to 90)

**Ex: sin60=cos(90-60) and vice versa**

if angle a and angle b r the acute angles of a right trinaglke, then sin a = cos b

New cards

33

rigid motion

A transformation that preserves distance and angle measures between objects. Examples include translations, rotations, and reflections.

New cards

34

rotations

New cards

35

dilation enlargement/reduction

create similar figures where the corresponding sides are in proportion and the corresponding angles are congruent

do not preserve distance or congruency

multiply the x and y values by the number

ex: (2,4) reduced by a half = (2,4)x1/2=(1,2)

New cards

36

composition of transformations

New cards

37

types of compisition trnadsfomagition

A composition of 2 reflections over 2 intersecting lines is equivalent to a ROTATION.

A composition of 2 reflections over 2 parallel lines is equivalent to a TRANSLATION.

New cards

38

rotational symmetry theorem

a regular polygon with 3 or more sides always has rotational symmetry , with rotations in increments. commonly referred as “mapping the figure onto itself”.

**360/n n=3 of sides**

New cards

39

circle equations

standard equation of a circle: where C,D and E are constants

center-radius equation of a circle: where (h, k) is the center and r is the radius

New cards

40

Chord

A line segment connecting two points on a curve or circle.

New cards

41

Secant

A line that intersects the circle in two or more points. This is a different secant than the secant in trigonometry.

New cards

42

Tangent

A line from outside a circle that intersects the border of a circle at one point but does not pass through the border to the circle’s interior. This is a different tangent than the tangent in trigonometry.

New cards

43

Central Angle

An angle whose vertex is at the center of a circle and whose legs are radii of the circle.

New cards

44

Inscribed Angle

An angle created when two chords of a circle share a point on that circle.

New cards

45

Circumscribed Angle

An angle created when two tangent lines to a circle intersect outside of that circle.

New cards