question

Parallelogram

answer

A quadrilateral in which both pairs of opposite sides are parallelogram.

question

Rhombus

answer

A parallelogram which has four congruent sides.

question

Rectangle

answer

A parallelogram which has four right angles.

question

Square

answer

A parallelogram which has four congruent sides and four right angles.

question

Kite

answer

A quadrilateral with two pairs of congruent sides and no congruent opposite sides; diagonals are perpendicular; symmetry; longer diagonal line of symmetry.

question

Trapezoid

answer

A quadrilateral with exactly one pairs of parallel sides.

question

Isosceles Trapezoid

answer

A trapezoid in which the nonparallel opposite sides (leg) are congruent; base angles are congruent; diagonals are congruent.

question

Consecutive Angles

answer

Angels that are opposite of each other.

question

Base Angles of Trapezoid

answer

The two angles that share a base.

question

Mid-segment of a Trapezoid

answer

Line segment connecting the midpoints of the legs; runs parallel to the bases of the trapezoid; its length is the average of the base length.

question

Properties of Parallelograms/Prove a Quadrilateral is Parallelogram

answer

Both pairs of opposite sides are parallel; both pairs of opposite sides are congruent; both pairs of opposite angles are congruent; consecutive angles are supplementary; the diagonals bisect each other; show that one pair of sides are simultaneously congruent and parallel.

question

Theorem 6-4

answer

If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on very transversal/

question

Properties of a Rhombus

answer

All the properties of a parallelogram; the diagonals bisect the vertex angles; the diagonals are perpendicular.

question

Properties of a Rectangle

answer

All the properties of a parallelogram; the diagonals are congruent(distance formula).

question

Properties of a Square

answer

All the properties of a parallelogram, rhombus and rectangle.

question

Circle

answer

The set of all the points equidistant from the given point.

question

Radius

answer

Segment from center to vertex.

question

Diameter

answer

A segment that contains the center of the circle and has both endpoints on the circle.

question

Central Angle

answer

Formed by two consecutive radii with the center as its vertex; 360/n (n= number of sides).

question

Semicircle

answer

Arc whose measure equals 180 degrees; named using three letters.

question

Minor Arc

answer

Arc who measure is between 0 and 180 degrees; named using three letters.

question

Major Arc

answer

Arc whose measure i s between 180 and 360 degrees; named using three letters.

question

Adjacent Arc

answer

Arcs in the same circle with any one point in common.

question

Circumference

answer

Distance around a circle; C=(pi)(d) or 2(pi)(r).

question

Arc Length

answer

Part of the circle's circumference.

question

Congruent Arc

answer

Arcs that have the same measure and length.

question

Sector of a Circle

answer

Fraction of a circle, formed by two radii and arc; named same as central angle.

question

Segment of a Circle

answer

Formed by arc and segment connecting end points.

question

Pythagorean Theorem

answer

(aa)+(bb)=(cc)

question

Area of a Rectangle

answer

A=bh

question

Area of a Parallelogram

answer

A=bh

question

Area of a Triangle

answer

A=1/2bh A= 1/2anSin<C

question

Area of a Trapezoid

answer

A=1/2h(b1 + b2)

question

Area of a Rhombus of a Kite

answer

A= 1/2(d1*d2)

question

Area of a Regular Polygon

answer

A= 1/2ap

question

Formula for Arc Length

answer

length of arc AB= measure of arc AB/360 *2(pi)(r)

question

Area of a Circle

answer

A=(pi)(r2)

question

Area of a Sector of a Circle

answer

measure of arc AB/360 * (pi)(r2)

question

Heron's Formula

answer

Find are if given all sides (SSS); are of a triangle; =the square root of(s(s-a)(s-b)(s-c) where s= a+b+c/2.

question

45-45-90 Triangle

answer

short leg=x; long leg=x hypotenuse=xroot2

question

30-60-90 Triangle

answer

short leg=x: long leg= xroot3; hypotenuse=2x

question

Ratio

answer

a comparison of two quantities measured in the same unit; will always be reduced to lowest terms and will have no units.

question

Proportions

answer

a statement that two ratios are equal; have three or more ratios are equal then they can be written as an extended proportion.

question

Scale Drawing

answer

A drawing that is either an enlargement or a reduction of an object.

question

Scale Factor

answer

The amount of enlargement or reduction is referred to as.

question

Quadratic Formula

answer

X= -b + - the square root of b2 -4ac/ 2a

question

Similar Polygons

answer

All corresponding angles must be congruent; all corresponding sides must be proportional.

question

Angle-Angle Similarity Postulate

answer

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

question

Side-Angle-Side Similarity Postulate

answer

If an angle of one triangle is congruent to one angle in another and the sides including the angles are proportional, then the triangles are similar.

question

Side-Side-Side Similarity Theorem

answer

If three sides of one triangle are proportional to corresponding sides in another triangle, then the triangles are similar.

question

Indirect Measurements

answer

Uses similar triangles and proportions to find distances that would otherwise be difficult to find.

question

Geometric Means

answer

A proportion in which the "means" in the proportion have the same value.

question

Theorem 8-3

answer

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

question

Side-Splitter Theorem

answer

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

question

Corollary to the Side Slitter Theorem

answer

If three parallel ones intersect two transversals then the segments intercepted on the transversal are proportional.

question

Triangle-Angle-Bisectors Theorem

answer

If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other sides of the triangle.

question

Similarity Ratio (Scale Factor):

answer

Ratio of corresponding parts of similar figures; comparison of LINEAR elements( lengths).

question

SOH-CAH-TOA

answer

Sine=opposite/hypotenuse; cosine= adjacent/hypotenuse; tangent=opposite/adjacent

question

Trig inverse

answer

Used to find angle measures

question

Angle of Elevation

answer

Is measured upward from the horizontal to line of sight.

question

Angle of Depression

answer

Is measure downward from the horizontal to line of sight.

question

Polyhedrons

answer

3 dimensional figure whose faces are polygons.

question

Faces

answer

Planes

question

Edges:

answer

Lines/segments

question

Vertices

answer

Points (corners)

question

Euler's Formula

answer

F+V=E+2

question

Platonic Sides

answer

Regular polyhedrons. They are regular because all of their faces are congruent regular polygons.

question

Tetrahedron

answer

4 faces

question

Hexahedron

answer

5 faces

question

Octahedron

answer

8 faces

question

Dodecahedron

answer

12 faces

question

Icosahedron

answer

20 faces

question

Net

answer

2 dimensional pattern that folds into a 3 dimensional figure.

question

Prism

answer

Polyhedron with 2, congruent, parallel faces and regular faces( lateral faces); named by the shape of its base.

question

Lateral Area

answer

Area of all lateral faces.

question

Surface Area

answer

Area of all faces( lateral faces plus both bases).

question

Right Cylinder

answer

A cylinder where the height is a side of the cylinder.

question

Oblique Cylinder

answer

A cylinder where the height is outside of the cylinder.

question

Lateral Area of a Cylinder

answer

2(pi)(r)(h)

question

Surface Area of a Cylinder

answer

2(pi)(r)(h) + 2(pi)(r2)

question

Volume of a Cylinder

answer

(pi)(r2)(h)

question

Slant Height

answer

The height that comes off of the base of a pyramid of cone that goes to the vertex.

question

Lateral Area of a Pyramid

answer

n(1/2sl)

question

Surface Area of a Pyramid

answer

n(1/2sl) + s2

question

Volume of a Pyramid

answer

1/3Bh

question

Lateral Area of Cone

answer

(pi)(r)(l)

question

Surface Area of a Cone

answer

(pi)(r)(l) + (pi)(r2)

question

Volume of a Cone

answer

1/3/(pi)(r2)(h)

question

Sphere

answer

The set of points in space equidistant from a given point(the center).

question

Surface Area of a Sphere

answer

4(pi)(r2)

question

Volume of a Sphere

answer

4(pi)(r3)/3

question

Tangent Line

answer

Line that intersects a circle in exactly one point (called the point of tangency)

question

Theorem 11-1

answer

A tangent line is perpendicular to a radius to the point of tangency

question

Theorem 11-3

answer

Two segments tangent to a circle from a point outside the circle are congruent.In addition to the two segments being congruent, line AB is congruent to line CB.

question

Chord

answer

A segment whose end points are on a circle.

question

Theorem 11-4

answer

Within a circle or congruent circles, congruent angles have congruent chords; within a circle or congruent circles congruent chords have congruent arcs; within a circle or congruent circles, congruent arcs have congruent central angles.

question

Theorem 11-5

answer

Within a circle or congruent circles, chord equidistant from the center are congruent and congruent chords are equidistant from the center.

question

Theorem 11-6

answer

In a circle, a diameter or radius is perpendicular to a chord if and only if it bisects the chord and its arc.

question

Inscribed Angles

answer

An angle in a circle whose vertex is on the circle and its sides are chords of the circle. An inscribed angle is never a central angle.

question

Theorem 11-9

answer

The measure of a inscribed angle is half the measure of the intercepted arc. Two inscribed angles that intercept tc are congruent. An angle inscribed in a semicircle is a right angle. The opposite angle of a quadrilateral inscribed a circle are supplementary.

question

Theorem 11-10

answer

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

question

Inscribed and Circumscribed

answer

A circle is inscribed in a quadrilateral and a quadrilateral is circumscribed around the circle.

question

Secant Lines

answer

A line that intersects a circle at exactly two points.

question

Theorem 11-11

answer

The measure of a vertical angle formed by two secant line sis half of the sum of the two intercepted arcs; the measure of the angle formed by two secant lines is half of the difference of the intercepted arcs; the measure of the angle formed by a secant line and a tangent line is half of the difference of the intercepted arcs; the measure of the angle formed by two tangent lines is half of the difference of the major arc and the minor arc. M

Geometry Semester 2 Final Study Guide – Flashcards

Unlock all answers in this set

Haven't found what you were looking for?

Search for samples, answers to your questions and flashcards