geometry regents

180(number of triangles-2)

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

360

360/number of triangles

no congruent sides

all sides are congruent

2 congruent sides

3 congruent angles

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

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

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

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

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

have the same slope

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

are points that lie of the same line

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

Formula: M =(x₁+x₂)/2, (y₁+y₂)/2.

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.

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

• 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

• 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

are congruent

supplemantary

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

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

• 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

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

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

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

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

• 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)

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.

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

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

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

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

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.

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

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

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