Geometry EOC Review

Perimeter of a triangle

The total distance around a triangle.

Inscribe

To draw a figure within another so that their boundaries touch but do not intersect.

Vertical Angles Theorem

Vertical Angles are congruent.

similarity transformation

a change in the position, shape, or size of the figure

inverse cosine

a function that gives the angle that has a given cosine ratio

inverse sine

a function that gives the angle that has a given sine ratio

inverse tangent

a function that gives the angle that has a given tangent

rigid motion

a transformation that does not change the size or shape

All right angles are ____________.

congruent

If a quadrilateral is a parallelogram then, its opposite sides are ______________.

congruent

If a quadrilateral is a parallelogram, then its opposite angles are _____________.

congruent

180 degree counterclockwise rotation

(-x, -y)

reflection across the origin

(-x, -y)

reflection across the y-axis

(-x, y)

reflection across y = -x

(-y, -x)

90 degree counterclockwise rotation

(-y, x)

reflection across the x-axis

(x, -y)

270 degree counterclockwise rotation

(y, -x)

reflection across y = x

(y, x)

Circumscribe

1. A triangle located round a polygon such as a circle. 2 To draw a figure around another, touching it at points but not cutting it.

Angle Bisector

A ray that divides an angle into two congruent angles

Properties of a Parallelogram

1. both pairs of opposite sides are parallel 2. both pairs of opposite sides are congruent 3. one pair of opposite sides are parallel and congruent 4. diagonals bisect each other 5. both pairs of opposite angles are congruent 6. consecutive angles are supplementary.

Volume of a cone or pyramid

1/3 the Area of the base times the height (NOT slant height)

Sum of the angles in a triangle

180°

composition of transformations

2 or more transformations

area of a triangle

A = 1/2bh

area of a parallelogram

A = bh

area of a rectangle

A = bh

Perpendicular Bisector

A line that is perpendicular to a segment at its midpoint.

Properties of a Square

All properties of parallelograms, rectangles, and rhombus.

Altitude

An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.

Side-Splitter Theorem

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

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a triangle then the segment is parallel to the third side and is half as long.

Alternate Exterior Angles Theorem

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

Alternate Interior Angles Theorem

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

Corresponding Angles Theorem

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

Same-Side (Consecutive) Interior Angles Postulate

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

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.

Side-Angle-Side Similarity (SAS~) Theorem

If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.

Side-Side-Side Similarity (SSS~) Theorem

If the corresponding sides of two triangles are proportional, then the triangles are similar.

Converse of the Pythagorean Theorem

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

Side-Side-Side (SSS) Postulate

If the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then AB+BC = AC.

Angle-Angle-Side (AAS) Theorem

If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA) Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangle are congruent.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Angle-Angle Similarity (AA~) Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Slopes of Parallel Lines

If two nonvertical lines are parallel, then their slopes are equal. If the slopes of two distinct nonvertical lines are equal, then the lines are parallel. Any two vertical lines or horizontal lines are parallel.

Slopes of Perpendicular Lines

If two nonvertical lines are perpendicular, then the product of their slopes is -1. If the slopes of two lines have a product of -1, then the lines are perpendicular. Any horizontal and vertical line are perpendicular.

Side-Angle-Side(SAS) Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Isosceles Triangle Theorem (Base Angles Thm)

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

Cavalieri's Principle

If two space figures have the same height and the same cross-sectional area at every level, then they have the same volume.

Area of a sector of a circle

The area of a sector of a circle is the product of the ratio (measure of the arc)/(360 degrees) and the area of the circle.

Midpoint Formula

The coordinate of the midpoint M of AB is (a+b)/2

Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Arc Addition Postulate

The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Degree

The mode your calculator should be in when solve trig ratios problems.

Area of a triangle

The number of square units it takes to fill the interior of a triangle.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180 degrees.

cosine ratio

adjacent/hypotenuse

Equilateral Triangle

all angles and sides equal

Isosceles Triangle

base angles are equal and two sides(legs) are equal

If a quadrilateral is a parallelogram, then its diagonals ____________ each other.

bisect

If the diagonals of quadrilateral ________________, then the quadrilateral is a parallelogram.

bisect each other

If an angle of a quadrilateral is supplementary to ___________________________, then the quadrilateral is a parallelogram.

both of its consecutive angles

Within a circle or in congruent circles, congruent arcs have congruent _______________.

central angles

If two segments are tangent to a circle from a point outside the circle, then the two segments are __________________.

congruent

If one pair of opposite sides of a quadrilateral is both _____________________, then the quadrilateral is a parallelogram.

congruent and parallel

Within a circle or in congruent circles, congruent central angles have ________________.

congruent arcs

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off _________________ on every transversal.

congruent segments

dilation

enlargement (greater than 1) or reduction (between 0 and 1)

If two figures congruent, then their areas are _____________.

equal

Properties of Trapezoids

exactly one pair of opposite sides are parallel and exactly two pairs of consecutive angles are supplementary

Right Triangle

follows Pythagorean theorem -angle opposite hypotenuse (longest side) = 90°

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

greater than

The measure of an angle formed by a tangent and a chord is ___________ the measure of the intercepted arc.

half

The measure of an angle formed by two lines that intersect inside a circle is ______________ of the measures of the intercepted arcs.

half the sum

If a parallelogram is a rectangle, then....

its diagonals are congruent, has four right angles, and it has all properties of a parallelogram.

If a parallelogram is a rhombus, then....

its diagonals are perpendicular, each diagonal bisects a pair of opposite angles, all sides are congruent, and it has all properties of a parallelogram.

If two angles of a triangle are not congruent, then the longer side lies opposite the _______ angle.

larger

If the square of the length of the longest side of a triangle is ____________ the sum of the squares of the lengths of the other two sides, then the triangle is acute.

less than

Through any three _______________ points there is exactly one plane.

noncollinear

Through any two points there is exactly _____________.

one line

If two distinct planes intersect, then they intersect in exactly ____________.

one plane

If two distinct lines intersect, then they intersect in exactly ____________.

one point

If two sides of a triangle are not congruent, then the larger angle lies _____________ the longer side.

opposite

tangent ratio

opposite/adjacent

sine ratio

opposite/hypotenuse

preimage

original image

The measure of an angle formed by two lines that intersect _____________ is half the difference of the measures of the intercepted arcs.

outside a circle

If two lines are parallel to the same line, then they are _______________.

parallel to each other

In a plane, if two lines are perpendicular to the same line, then they are ______________.

parallel to each other

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is _________________.

parallelogram

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a _________________.

parallelogram

If a line is tangent to a circle, then the line is _________________ to the radius at the point of tangency.

perpendicular

If a line bisects the vertex angle of an isosceles triangle, then the line is also the ___________________ of the base.

perpendicular bisector

Quadrilateral

polygon with 4 sides

If the diagonals of a parallelogram are congruent, then the parallelogram is a _____________.

rectangle or square

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a ___________________.

rhombus or square

If the diagonals of a parallelogram bisects a pair of opposite angles, then the parallelogram is a ______________.

rhombus or square

isometry

rigid transformation

A composition of reflections across two intersecting lines is a _____________________.

rotation

congruence

same size and shape

opposite leg to angle A

side y

adjacent leg to angle A

side z

translation

slide

If a quadrilateral is a parallelogram, then its consecutive angles are _______________.

supplementary

The opposite angles of a quadrilateral inscribed in a circle are ____________________.

supplementary

If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is ________________ to the circle.

tangent

angle of elevation

the angle between a horizontal line (like the ground) and your line of sight, when you look up at an object

angle of depression

the angle between a horizontal line and your line of sight, when you look DOWN at an object

opposite leg

the leg across from a given acute angle in a right triangle

adjacent leg

the leg that touches a given acute angle in a right triangle

segment of a circle

the part bounded by an arc and the segment joining its endpoints

Volume of a prism

the product of the AREA of the base and the height

image

the result of a transformation

hypotenuse

the side opposite the right angle in a right triangle

Surface Area of a Pyramid

the surface area of a regular pyramid is the sum of the lateral area and the area "B" of the base.

Surface Area of a Cone

the surface area of a right cone is the sum of the lateral area and the area of the base.

Surface Area of a Cylinder

the surface area of a right cylinder is the sum of the lateral area and the areas of the two bases.

Surface Area of a Prism

the surface area of a right prism is the sum of the lateral area and the areas of the two bases

Volume of a Cylinder

the volume of a cylinder is the product of the area of the base and the height of the cylinder

The composition of reflections across parallel lines is a ___________________.

translation