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
