Geometry 📏

(12 sided polygon). Sides EF and GH are extended so that they meet at point O in the exterior of a polygon. Find M<FOG

FOG=160

Find GH. Round to the nearest hundredth

GH=22.46

Describe the three dimensional figure that can be made from the given net

Hexagon Prism

Classify the figure. Name the vertices,edges, and base

Vertices -A,B,C,D, F Edges-AB,AC,AD,AF,FB,BC,CD,DF Bases-D,C,B,F

The radius and height of the cylinder are multiplied by 4 m. describe the effect on the volume

Volume is multiplied by 3

The door on a spacecraft is formed with 6 straight panels that overlap to form a regular hexagon. What is the measure of <YXZ

YXZ= 60

inscribed circle

a circle in which each side of the polygon is tangent to the circle

net

a diagram of the surfaces of a 3D figure that can be folded to form the 3D figure

Tangent of a circle

a line that is in the same plane as a circle and intersects the circle at exactly one point

common tangent

a line that is tangent to two circles

cube

a prism with 6 square faces

Rhombus

a quadrilateral with 4 congruent sides

Rectangle

a quadrilateral with 4 right angles

square

a quadrilateral with 4 right angles and 4 congruent sides

kite

a quadrilateral with exactly 2 pairs of congruent consecutive sides

trigonometric ratio

a ratio of the sides of a right triangle

external secant segment

a secant segment that lies in the exterior of the circle with one endpoint on the circle

secant segment

a segment of a secant with at least one endpoint on the circle

tangent segment

a segment of a tangent with one endpoint on the circle

subtend

a segment of arc subtends an angle if the endpoints of the segment or arc lie on the sides of the angles

diagonal

a segment that connects any two nonconsecutive vertices

central angle

an angle whose vertex is the center of the circle

intercepted arc

an arc that consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between the endpoints

arc

an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them

concave

any part of a diagonal contains points in the exterior of the polygon

Adjacent arcs

arcs of the same circle that intersect at exactly one point

radius of a sphere

connects the center of the sphere to any point on the sphere

concentric circle

coplanar circles with the same center

Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth

cos X = 12/15 =0.80

The radius of the sphere is multiplied by 1/2. Describe the affect on the volume

divide by 8

great circle

divides a sphere into two hemispheres

base

each of the parallel sides

side of a polygon

each segment that forms a polygon

face

flat surface

cone

formed by a circular base and a curved surface that connects the base to a vertex

pyramid

formed by a polygonal base and triangular faces that meet at a common vertex

cylinder

formed by two parallel congruent circular bases and a curved surface that connects the bases

Prism

formed by two parallel congruent polygonal faces called bases

isosceles trapezoid

if the legs of a trapezoid are congruent

equal vectors

if they are in the same or parallel lines their direction are the same and the lengths are equal

Volume

number of non overlapping unit cubes of a given size

base of a trapezoid

one of a pair of consecutive angles whose common side is a base of the trapezoid

base a trapezoid

one of the two parallel sides of the trapezoid

Tangent

ratio of the opposite to the adjacent side of a right-angled triangle

Identify the secant that intersects A.

secant BC

edge

segment that is the intersection of 3 or more faces

Use your calculator to find the trigonometric ratios sin 79, cos 47 , and tan 77. Round to the nearest hundredth.

sin79= 0.98, cos47 =0.68 , and tan77 =4.33

Use a special right triangle to write tan 60° as a fraction

tan(60°) = √3/1

angle of elevation

the angle formed by a horizontal line and the line of sight to an object above the horizontal line

geometric mean

the central number in a geometric progression

vertex of the polygon

the common endpoint of two sides

Midsegment of a trapezoid

the segment whose endpoints are the midpoints of the legs of the trapezoid

interior of a circle

the set of all points inside the circle

exterior of a circle

the set of all points outside the circle

Cosine

the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.

resultant vector

the vector sum of two or more vectors

Sine

trig. function that is equal to the ratio of the side opposite to the given angle

congruent arcs

two arcs that have the same measure

base angles

two consecutive angles whose common side is a base

tangent circle

two coplanar circles that intersect at exactly one point

parallel vectors

vectors with the same or opposite direction

What is the horizontal distance between the eagle and its prey? Round to the nearest foot

1120ft

Find the volume of the composite figure. Round to the nearest hundredth

113.04 (composite figure)

Find the volume of a cylinder with a base area of 25 π in^2 and height equal to the radius. Give your answer both in terms of π and rounded to the nearest tenth

125 in^3 = 392.7 (cylinder)

Find the volume of a rectangular pyramid with length 11m ,width 7m, and height 8m. Round to the nearest tenth if necessary

205.3m (rectangular pyramid)

What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter

402m

Find the volume of a right rectangular prism with length 12 in, width 10 in, and height 6 in . Round to the nearest tenth, if necessary

720 in (rectangular prism)

Find the volume of the composite figure. Round to the nearest tenth.

88.0 cm (composite figure)

segment of a circle

A region inside a circle bounded by a chord and an arc

AB and AC are tangent to P. find AB

AB= 11/2

Find measure AC

AC=30

Find the point of tangency and write the equation of the tangent line at this point

B (3,0) equation of the tangent line X=3

Draw a pattern that can be used to create a cylinder with diameter equal to half the height

"Rectangle with to cirlces on the end"

Find the measure of each interior angle of a regular 45-gon

(1-2) x 180= 172

Graph the equation (x-3)^2 + (y+2)^2 = 25

*choose a graph

What is the length of the runaway? Round to the nearest tenth of a kilometer

1.2km

Jessie decides to make an angle between the ramp and the ground 15. to the nearest hundredth of a foot,find the length of the ramp

10.82ft

TRSU is a rhombus. Find SU

5x+2 = 2x+5 3x=3 x=1 SU=7

MNOP is a parallelogram. Find MP

5x=3x+12 2x=12 x=6 MP=30

Secant

A line that intersects a circle in two points

Parallelogram

A quadrilateral with 2 pairs of parallel sides

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Vector

A quantity that has magnitude and direction

chord

A segment whose endpoints lie on a circle

sphere

A solid shape that is perfectly round like a ball. No faces, edges, or vertices.

semicircle

An arc of a circle whose endpoints lie on a diameter

major arc

An arc of a circle whose points are on or in the exterior of a central angle

minor arc

An arc of a circle whose points are on or in the imterior of a central angle

Classify each angle in the diagram as an angle of elevation or an angle of depression

Angle of elevation = 📐1 ,📐3 Angle of depression= 📐2,📐4

The circle graph shows the colors of automobiles sold at a car dealership. Find measure CD

CD=36

Find measure CFB

CFB =30

A sandwich ship sells cheese. How can the chef cut a square pyramid shape piece of cheese to make slices that are squares

Cut parallel to the base

Tell whether the figure id a polygon? (if it is a polygon ,name it by the number of its sides)

Decagon

Tell whether the polygon is regular or irregular . Tell whether it is concave or concex

Irregular Concave

In kite PQRS, m<QPO=50 and m<QRO=70. Find m<PSR

PSR=60

In parallelogram RSTU ,UR=25,RX=16, and m<STU=42.4. FInd ST,XT, and m<RST

ST=25, RST=137.6 , and XT=16

Use a calculator to find the trigonometric ratios sin 123,cos 95, and tan 125. Round to the nearest hundredth

Sin 123 =0.84 , Cos 95 =0.09 , and Tan 125= -1.43

Find the sine and cosine of the acute angles in the right triangle

Sin A = 45/53 Cos A =25/53 Sin B = 25/53 Cos B = 45/53

use your calculator to find the angle measure Sin^-1 (0.7), Cos^-1 (0.3) , and Tan^ -1(38.4) to the nearest tenth of a degree

Sin ^-1(0.7)= 44.4 Con ^-1(0.3) = 72.5 Tan ^-1(38.4) =88.5

Find sin<A to the nearest hundredth

Sin<A =0.45

angle of depression

The angle formed by a horizontal line and the line of sight to an object below the horizontal line

Describe the cross section

The cross section is a circle

hemisphere

half of a sphere

convex

if no diagonal contains points in the exterior

Find the measure of each interior angle of a regular decagon

m< 36

arc length

the distance along an arc measured in linear units

cross section

the intersection of a 3D figure and a plane

magnitude

the length of the vector, while the direction is the way its pointing

direction

the measure of the angle it makes with a horizontal line

legs

the nonparallel sides

component form

the ordered pair that describes the changes in the x- and y-values

point of tangency

the point of intersection of a circle or sphere with a tangent line or plane

vertex

the point that is the intersection of three or more faces

sector of a circle

the region bounded by two radii of the circle and their intercepted arc