# 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.

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

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…

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

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

(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?

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.

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.

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…

Properties of Parallelograms

Properties of Rectangles

Properties of Squares

Properties of Rhombus

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

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

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

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

Properties of Parallelograms

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

Properties of Rectangles

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

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…

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

Properties of Parallelograms

Properties of Rectangles

Properties of Squares

Properties of Rhombus

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

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

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

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

Properties of Parallelograms

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

Properties of Rectangles

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

equation of a circle

angle measures of a quadrilateral in a…

intersecting chords rule

secant-secant rule

(x - h)² + (y - k)² = r²

opposite angles add up to 180°

(seg part)(seg part) = (seg part)(seg part)

(whole)(exterior) = (whole)(exterior)

equation of a circle

(x - h)² + (y - k)² = r²

angle measures of a quadrilateral in a…

opposite angles add up to 180°

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…

Midpoint

Angle Bisector

Complementary

Supplementary

a point that cuts a line segment into two congruent segments

a ray that cuts an angle into two congruent angles

two or more angles whose sum is 90 degrees

two or more angles whose sum is 180 degrees; also called a lin…

Midpoint

a point that cuts a line segment into two congruent segments

Angle Bisector

a ray that cuts an angle into two congruent angles