# geometry regents review

##### SETS

Tangent

Secant

Intersection of a tangent and a radius

Equation of a circle

intersects a circle in only 1 place.

intersects a circle in 2 places.

form right angles when they intersect.

x minus h squared plus y minus k squared equals radius squared.

Tangent

intersects a circle in only 1 place.

Secant

intersects a circle in 2 places.

central angle =

inscribed angle =

angle by tangent/chord =

arc length formula

arc

1/2 arc

half arc

central angle =

arc

inscribed angle =

1/2 arc

perpendicular lines

diameters/radii and tangents

corresponding sides of similar triangle…

legs in an isosceles shape are

form right angles

form right angles

in proportion

equal

perpendicular lines

form right angles

diameters/radii and tangents

form right angles

Unit One: Basic Geometry/Constructions

Equilateral Triangle

Isosceles Triangle

Angle Bisector

...

All sides are congruent

2 of the sides are congruent

Line that cuts an angle in half

Unit One: Basic Geometry/Constructions

...

Equilateral Triangle

All sides are congruent

Collinear Points

complementary angles

supplementary angles

exterior angle theorem

points that lie on the same line

have a sum of 90 degrees

have a sum of 180 degrees

in a triangle; two interior angles equal the opposite exterior…

Collinear Points

points that lie on the same line

complementary angles

have a sum of 90 degrees

perpendicular lines

diameters/radii and tangents

corresponding sides of similar triangle…

legs in an isosceles shape are

intersect to form right angles

intersect on a circle to form right angles

in proportion

equal

perpendicular lines

intersect to form right angles

diameters/radii and tangents

intersect on a circle to form right angles

Tangent

Secant

Intersection of a tangent and a radius

Equation of a circle

intersects a circle in only 1 place.

intersects a circle in 2 places.

form right angles when they intersect.

x minus h squared plus y minus k squared equals radius squared.

Tangent

intersects a circle in only 1 place.

Secant

intersects a circle in 2 places.

Collinear Points

complementary angles

supplementary angles

exterior angle theorem

points that lie on the same line

have a sum of 90 degrees

have a sum of 180 degrees

in a triangle; two interior angles equal the opposite exterior…

Collinear Points

points that lie on the same line

complementary angles

have a sum of 90 degrees

(3,4,5) (5,12,13) (8,15,17) (7,24,25)

Where the perpendicular bisectors inter…

Where the angle bisectors intersect

Where the altitudes intersect

Name 3 Pythagorean triples

What is the circumcenter of a triangle?

What is the incenter of a triangle?

What is the orthocenter of a triangle?

(3,4,5) (5,12,13) (8,15,17) (7,24,25)

Name 3 Pythagorean triples

Where the perpendicular bisectors inter…

What is the circumcenter of a triangle?

congruent

similar

pre-image

image

figures with the same shape, angles, sizes, sides; two or more…

two or more figures with corresponding angles that are equal i…

original figure that is to be transformed

figure that is formed when each point in an original figure is…

congruent

figures with the same shape, angles, sizes, sides; two or more…

similar

two or more figures with corresponding angles that are equal i…

Reasons for Proofs

Reasons for Proofs

Reasons for Proofs

Reasons for Proofs

Reflexive Property

Alternative Interior Angles are congruent

Rights angles are congruent

Opposite sides of a parallelogram are congruent and parallel

Reasons for Proofs

Reflexive Property

Reasons for Proofs

Alternative Interior Angles are congruent

Tangent

Secant

Intersection of a tangent and a radius

Equation of a circle

intersects a circle in only 1 place.

intersects a circle in 2 places.

form right angles when they intersect.

x minus h squared plus y minus k squared equals radius squared.

Tangent

intersects a circle in only 1 place.

Secant

intersects a circle in 2 places.

Quadrilateral

Trapezoid

Parallelogram

Rectangle

A four sided figure

Quadrilateral with at least one pair of parallel sides

Opposite sides are parallel and congruent... Diagonals bisect eac…

Parallelogram with 4 right angles ... Diagonals intersect at 90 d…

Quadrilateral

A four sided figure

Trapezoid

Quadrilateral with at least one pair of parallel sides

acute angle

acute triangle

adjacent angles

altitude

an angle whose degree measure is less than 90 and greater than…

a triangle with three acute angles

two angles with the same vertex, a common side and no interior…

in a triangle, a segment that is perpendicular to the side whi…

acute angle

an angle whose degree measure is less than 90 and greater than…

acute triangle

a triangle with three acute angles

congruent

similar

pre-image

image

figures with the same shape, angles, sizes, sides; two or more…

two or more figures with corresponding angles that are equal i…

original figure that is to be transformed

figure that is formed when each point in an original figure is…

congruent

figures with the same shape, angles, sizes, sides; two or more…

similar

two or more figures with corresponding angles that are equal i…

sum of interior angles

each interior angle

sum of exterior angles

each exterior angle

180(n-2)

180(n-2)/n

360

360/n

sum of interior angles

180(n-2)

each interior angle

180(n-2)/n

pythagorean theorem

scalene triangle

isosceles

equilateral

- only used for right triangles ... - c must be the hypotenuse

no congruent sides

2 congruent sides

3 congruent sides

pythagorean theorem

- only used for right triangles ... - c must be the hypotenuse

scalene triangle

no congruent sides

Properties of Parallelograms

Rectangles, squares, and rhombi are all:

Properties of Rectangles

Properties of Squares

1) Opposite sides are congruent... 2) Opposite angles are congrue…

parallelograms so they have all the properties of a parallelog…

1) Opposite sides are congruent... 2) Opposite angles are congrue…

1) All sides are congruent... 2) Opposite angles are congruent... 3)…

Properties of Parallelograms

1) Opposite sides are congruent... 2) Opposite angles are congrue…

Rectangles, squares, and rhombi are all:

parallelograms so they have all the properties of a parallelog…

perpendicular lines

diameters/radii and tangents

corresponding sides of similar triangle…

legs in an isosceles shape are

form right angles

form right angles

in proportion

equal

perpendicular lines

form right angles

diameters/radii and tangents

form right angles

perpendicular lines

diameters/radii and tangents

corresponding sides of similar triangle…

legs in an isosceles shape are

form right angles

form right angles

in proportion

equal

perpendicular lines

form right angles

diameters/radii and tangents

form right angles

acute angle

acute triangle

adjacent angles

adjacent arcs

an angle whose measure is between 0° and 90°

a triangle with three acute angles

two coplanar angles that have a common side and a common verte…

arcs that are on the same circle and have exactly one point in…

acute angle

an angle whose measure is between 0° and 90°

acute triangle

a triangle with three acute angles

line axiom

the distance assignment postulate

the segment existance postulate

line segment extension postulate

two points determine a line:... given any two distinct points, ex…

to every pair of distinct points there corresponds a unique po…

given ray XY and line segment AB there exists exactly one poin…

given any two distinct points A and B, there exists a point C…

line axiom

two points determine a line:... given any two distinct points, ex…

the distance assignment postulate

to every pair of distinct points there corresponds a unique po…

segment bisector

a midpoint

an angle bisector

perpendicular lines intersect to form

intersects a segment at its midpoint

divides the segment into two congruent segments, each half the…

divides an angle into two congruent angles

right angles

segment bisector

intersects a segment at its midpoint

a midpoint

divides the segment into two congruent segments, each half the…

Segment

Radius

Circle

Construction: Equilateral Triangle

The ____________connecting points A and B is the set consistin…

Segment from the center of a circle to a point on the circle.

Given a point on C in the plane and a number r > 0, the ______…

Construct an equilateral triangle using the given segment...…

Segment

The ____________connecting points A and B is the set consistin…

Radius

Segment from the center of a circle to a point on the circle.

Quadrilateral

Trapezoid

Isosceles trapezoid

Rectangle

4 sided polygon... sum of interior angles 360

at least 1 pair of // sides

each pair of base angles are con.... diagonals are con.... one pair…

all angels are right angles... diagonals are con.

Quadrilateral

4 sided polygon... sum of interior angles 360

Trapezoid

at least 1 pair of // sides