EOC Review Game- Paris & Daneris

Area of a sector

(m/360)(πr^2) where m is the measure of the central angle and r is the radius.

Write the equation of a circle with radius √10ft. and center (-4,-3).

(x+4)^2+(y+3)^2=10

Write the equation of a circle with center (3, -2) and radius 5 in ( 10-5)

(x-3)^2 + (y+2)^2 =25

Equation of a circle

(x-h)²+(y-k)²=r², (h,k) is the center of the circle, r is the radius of the circle.

A can of sweet peas at the local grocery store has a radius of one inch and a height of two inches. How much paper is used for the label on the can of peas?(14-5)

12.57 in ^2

Two sides of a triangle measure 18cm and 30cm. What is the range of possible measures for the side of this triangle?

12<AB<48

A merry-go-round has a diameter of 24 feet. To the nearest tenth of a foot, what distance does the merry-go-round cover when it rotates an angle of 76? ( use 3.14 for π) ( 12-4)

15.90

Simplify the square root. 3√6 × √12 (no chapter just important lesson)

18√2

The roof of the house down the road is in the shape of a square pyramid. The length from the the gutter to the top is 15ft. and the length of gutter on one side is 18ft. with no overlap. One bundle of shingles covers 25 square feet. How many bundles should you buy to cover the roof?

22 Bundles

The measure of an exterior angle of a regular polygon is 15. How many sides does this polygon have?

24 sides

Find the sum of the interior angles of a 18-gon.

2880 (degrees)

Lateral Area of a Cylinder

2πrh

Surface Area of a Cylinder

2πrh+2πr²

M partitions line CD in a ratio 3:5 find k (1-6)

3/8

What is the order of symmetry for a regular hexagon?(Symmetry)

6

An arc measures 125 in a circle with a radius of 36 centimeters. What is the length of the arc to the nearest tenth? (use 3.14 for π) (12-3)

78.5

Central angle of a circle

An angle whose vertex is the center of the circle.

Convex

A line segment drawn between any two points on the shape will always lie inside the shape (all edges pointing outwards).

Concave

A polygon is concave if any part of a diagonal contains points in the exterior of a polygon.

Kite

A quadrilateral with exactly two pairs of congruent consecutive sides.

Diameter of a circle

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

Radius of a circle

A segment that has one endpoint at the center and the other endpoint on the circle (half the diameter).

In parallelogram JKLM, LM=86 millimeters, LK=100 millimeters, and m< JML= 42 find each measure. (6-2) A. JM B. KJ C.m< KJM D.m<LKJ E.m<MLK

A. 100 B. 86 C. 138 D. 42 E. 138

Given Triangle KTR is congruent to Triangle BAN Complete the statement below correctly. ( 4-4) A. < A is congruent to B. Line RK is congruent to C. Line NA is congruent to

A. < T B. Line NB C. Line RT

The diameter of a circle is 15ft. Find the area of this circle. (Write answer in form of π)

A= π56.25 or A= π7.5^2

Equidistant

At equal distances.

Find the circumference and area. *Radius is 8cm* (Use calculator's value of π, round to the nearest 10.)

Circumference: ≈ 50.3cm Area:≈ 201.1cm^2

Semi-circle

Half of circle, (equals 180).

Converse of the Perpendicular Bisector Theorem

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

Converse of the Angle Bisector Theorem

If a point is in the interior of an angle is equidistant from the sides of the angle, then it lies on the bisector of the angle.

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Perpendicular Bisector Theorem

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

The Hinge Theorem (SAS Inequality Theorem)

If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.

Converse of the Hinge Theorem (SSS Inequality)

If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side.

30-60-90 Triangle Theorem

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.

45-45-90 Triangle Theorem

In a 45-45-90 triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given: KLAR is a parallelogram, line LR and line KA intersect at M, LM= ( 9x-5) and MR= (8x + 3). Find LR ( 9-5 )

LR = 134

Major Arc of a circle

Larger than a semi-circle (more than 180).

Kate claims she can make a triangle from three pieces of wood that are 15 inches, 9 inches and 6 inches. Is this possible? Justify your answer: ( 5-5 )

No because the sum of the two shortest sides is less than the longest side.

Minor Arc of a circle

Smaller than a semi-circle (less than 180).

M, K and T are collinear, T is between M and K. TK =18cm TM=(4x + 3)cm and MK= (6x + 4)cm. Find TM ( 1-1)

TM = 37

Area of a circle

The amount of space inside the boundary of a 2 dimensional object A=πr²

Isosceles Trapezoid

The base angles are equal and therefore the left and right side lengths are also equal.

Circumference

The distance around a circle C=2πr or C=πd

The base of the lampshade is a regular hexagon with the side length of 8 inches and a slant height of 10 inches. Estimate the amount of glass needed to make the lampshade.

The glass needed is 240in.sq.

Surface Area

The outside part or uppermost layer of something (often used when describing its texture, form, or extent).

Circle

The set of all points in a plane that are the same distance from a given point called the center.

Volume of a pyramid

V=1/3Bh

Volume of a prism

V=Bh

In a 30-60-90 triangle if the hypotenuse is 20 and x is the SL and y is the LL what are the values of x and y? ( 5-4)

X= 10 Y= 10√3

The diagonals of a quadrilateral form right angles and its side lengths are 4,4,6 and 6. Could this quadrilateral be a kite? `

Yes because it's consecutive.

Triangle REN is congruent to triangle YAL. Complete the sentence correctly. a. <L ≅ ___________ b. segment RN ≅ _________ c. segment AY ≅ __________

a. <N b. segment YL c. segment ER

Distance Formula

d = √[( x₂ - x₁) ^2+ (y₂ - y₁)^2]

The area of this circle is 113.04in^2. Find the diameter of this circle. (Use 3.14 for π)

d=12in

The surface area of the square pyramid is 85 square meters. The base length is 5 meters. Determine the slant height.

l=6m.sq.

< GHR and < KHR form a linear pair, m < GHR=(3x-2) and m < KHR ( 11x+ 14) Find m < GHR. (3-4)

m < GHR= 34

Given ABCD is a parallelogram, m<A = (7x+9), m<B = (3y-8), m<D (3x+1) and m<C = (6y+8). Find the m<B

m<B= 52 (degrees)

Given: Triangle TRA is congruent to triangle PEl, m<L= 120 and m<R =24. Find m<P

m<P = 36

Determine the radius of a cone that has a lateral area of 70π and a total surface area of 120π.

r=5√2

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints. L (4, 0) and M (-2, 3). (5-1)

y= - 3/2 + 2(x-1)