Geometry Final Test Review/Notes

(8,10) use a graphing calculator to calculate slope!

The midpoint between AB is M(3,7). If A is (-2, 4), what is the coordinate of B?

(-2,3) the formula for equation of a circle is: (x-h)^2 + (y-k)^2 = r^2 *don't forget that double negatives turn into a positive (that happened in this question)*

What is the center of the circle described by this equation? (x+2)^2 + (y-3)^2 = 36

square root of 18 4-1 = 3 -5-(-8)= 3 3^2+3^2= 18 don't forget to square root your answer!

What is the distance between (4,-5) and (1, -8)?

4 first you have to solve this algebraically

What is the radius of the circle described by this equation? x^{2}+y^{2}-10x+2y+10=0

69.3 formula for volume of a hexagonal pyramid: v= square root of 3 divided by 2 * a^2 * h in this case, 24/6 will get you the side length of 4 if you plug in the 4 and the 5 into the equation for volume, you should get the answer of 69.3

Find the volume in cubic inches of a regular hexagonal pyramid with a base perimeter of 24 inches and a pyramid height of 5 inches. Round your answer to the nearest hundredth

Perpindicular same graph w/ slope of 0.2 (1/5)

For the equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither? (y-3) = -5(x-4)

70 180-40=140 140/2=70

In an isosceles triangle ABC, AB = AC. If angle A is 40 degrees, what is the measure of angle C?

i suggest desmos graphing calculator (this is very very helpful for visualizing stuff)

need a graphing calculator?

a.) 3817.04 formula for volume of a cylinder: pi*r^2*h in this case: pi*9^2*15 = 3817.04 b.) 1272.34 formula for volume of a cone: 1/3*pi*r^2*h in this case: 1/3*pi*9^2*15 = 1272.34 c.) 1/3

A cylinder has radius 9 inches and height 15 inches. A cone has the same radius and height. a. Find the volume of the cylinder. b. Find the volume of the cone. c. What fraction of the cylinder's volume is the cone's volume?

square root of 9/324 here, you have to do 324 pi * k^2 = 9 pi *don't forget the pi's will cancel each other out* so divide: 9/324, but don't forget to square root!

A monster truck wheel has an area of `324\pi` square inches. A toy company wants to create a scaled copy of the monster truck with a wheel area of `9\pi\ `square inches. What scale factor should the company use?

162 first, solve for the k for the suface area 22 * k = 198 198/22 = 9 so now we know that k = 9 to solve for the volume of the new image, we have to do... 6 * 9 cubed = answer

A solid has volume 6 cubic units and surface area 22 square units. The solid is dilated, and the image has surface area 198 square units. What is the volume of the image?

274.5 use trig here to find its base, working with side length 4 and angle 65 tan(65)/1 = x/4 then use that to solve for the whole volume of the prism. so 4 times new side length you solved for, then divide by 2 then base times 16, gives you the volume

A triangular prism has height 16 units. The base of the prism is shown in the image. What is the volume of the prism? Round your answer to the nearest hundredth

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

AAS (congruence theorem)

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 triangles are congruent

ASA (congruence theorem)

Neither it's the same graph here as the last one, so 5x is neither parallel or perpindicular to 0.2

For the equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither? y= 5x-3

Parallel the slope of the graph it wants you to compare to is 1/5, so 0.2

For the equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither? y=0.2x

74 you have to do trig here in this case, x/z was a/h so...cos inverse on a calculator doing cos inverse of 0.28 will give you 73.a bunch of numbers. rounded to the nearest degree is 74

For the right triangle shown, x/z = 0.28. What is the measure of `alpha`to the nearest degree?

What is the measure of arc DE?: 40 (its inscribed angle is 20) What is the measure of angle DCE?: 40: (its inscribed angle is 20) What is the measure of angle BAE?: 25 (alternate interior w/ FBA) What is the measure of arc FB?: 80 (add up the other angles to find the middle arc- 50+50=100/180-100=80)

In Circle C, AE is a diameter and FB is parallel to AE. If arc AF = 50 degrees and angle DAE = 20 degrees, can you find the other missing angles in the picture.

3 for similar triangles...keep it organized and consistent. for example, in this case I did small/medium (1st triangle): 6/12 = x/12: small/medium(2nd triangle) x=3

In right triangle ABC, altitude CD with length 6 is drawn to its hypotenuse. We also know AD = 12. What is the length of DB?

3.56 because this has a right triangle, just do trig multiply the two side lengths (one of them you should have solved for with the trig) then you should divide by 2 to get the area

Line CD is tangent to the circle centered at A. What is the area of the triangle if angle CAD = 24 degrees and the radius of the circle is 4? Round your answer to the nearest hundredth

not enough info/not applicable to any theorem (most of the times the figures will not include enought angle measures or side lengths to determine)

NEI

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

SAS (congruence theorem)

if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

SSS (congruence theorem)

3.5 this is a nested triangle, so you should do proportions in this case it was, 3/6 on one side and x/7 on the other cross multiply and you get 21/6, which is 3.5

Segment A'B' is parallel segment AB. What is the length of segment BB'?

there will be an X next to the correct answers *remember perpendicular lines have opposite reciprocal slopes* 3x-2y=4 2x+3y=6 2x-3y=8 X (y-4) = 2/3 (x-6) X (y-2) = -3/2 (x-8) y- 2/3x X y= 3/2x + 3

Select all equations whose graphs are lines perpendicular to the graph of `3x+2y=6`

here you do pythagorean theorem i'll put an 'X' next to the correct answers Triangle ABC with AB = 30, BC = 40, and AC =50 X Triangle XYZ with XY = 1, YZ = 1, and XZ = 2 Triangle EFG with EF = 8, FG = 15, and EF 17 X Triangle LMN with LM = 7, MN = 24, and LN = 25 X Triangle QRS with QR = 4, RS = 5, and QS = 6

Select all of the right triangles

17 -an inscribed angle is half of the central angle

The Measurement of Angle CAB is `34°`. What is the measurement of angle BDC?

(-4,-2) using a graphing calculator here will help to solve it visually with transformations

The coordinate A(5, 6) is reflected over the y-axis to form A'. A' is then translated to the right 3, and down 2 to make A''. A'' is then rotated 90 degrees counter-clockwise about the origin to form A'''. What is the location of A'''?

36 45-45-90 triangle tells us that the side length is 6 area: 6 squared

The diagonal of a square is `6\sqrt{2}`. What is the area of the square in units squared?

9.42 formula for sector area: pi*r^2 in this case, 30/360 = 0.08333333 0.833333 number * pi * 6^2 this should get you your answer

The measure of the central angle that forms a sector of a circle is 30°. If the radius of the circle is 6 cm, what is the measure of the sector area, in cm squared? Round to the nearest hundredth.

12.57 when finding the arc length, use the equation for circumference: 2*pi*radius 24/360= 0.6666667 (this is the part of the circle you're working with) answer * 2 * 30 = 4 (don't forget to add the pi) 4 pi = 12.57

The measure of the central angle that intercepts some arc is 24°. If the radius of the circle is 30 cm, what is the measure of the arc length, in cm? Round to the nearest hundredth?

27.21 -Divide 24 by 3 to get the side length of 8

The perimeter of an equilateral triangle is 24 units. What is the area of the equilateral triangle in units squared?

100

The quadrilateral is a parallelogram. Find the measure of angle 1.

18 first thing: these are isoceles triangles 360-84=276 276/2=138 (this will get you the angles for the other two triangles 138 + 24 = 162 180-162 = 18

Triangle ACD and BCD are isosceles. Angle DBC has a measure of 84 degrees and angle BDA has a measure of 24 degrees. Find the measure of angle BAC.

27 solve here for the height scale factor (k), and then do 12 * k^2

Two parallelograms are similar. The height of the smaller parallelogram is 4 cm and the height of the larger parallelogram is 6 cm. If the area of the smaller parallelogram is 12 cm squared, what is the area of the larger parallelogram?

17 solve for angles in a kite 60/2 = 30 133+30= 163 180-163 = 17

WXYZ is a kite. Angle WXY has a measure of 133 degrees and the angle ZWX has a measure of 60 degrees. Find the measure of angle ZYW.