Geometry

1 2 3

m GHD = 1/2 (DG-DE) m BAC = 2 (m DGE) m ADH = 90 m DHE = 1/2 (DGE - DE) m DGE > m BFC DGE is a right triangle

a

180 Degree Clockwise Rotation (r-180) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

a

180 Degree Counter Clockwise Rotation (r180) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

b

270 Degree Clockwise Rotation (r-270) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

c

270 Degree Counter Clockwise Rotation (r270) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

Across from 90 degree angle 2x Across from 30 degree angle x Across from 60 degree angle x*squareroot of 3

30 60 90 Triangle sides

Across from 90 degree angle x * squareroot of 2 Across from 45 degree angle x Across from 45 degree angle x

45 45 90 Triangle sides

c

90 Degree Clockwise Rotation (r-90) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

b

90 Degree Counter Clockwise Rotation (r90) a. (-x, -y) b. (-y, x) c. (y, -x) d. (-y, -x)

d

A cylinder and a cone have the same diameter. The cylinder is 12 times the height of the cone. How many of the cone could fit in the cylinder? a. 6 b. 4 c. 24 d. 36

b

A large sphere has a diameter 4 times the diameter of a smaller sphere. How are the volumes of the 2 spheres related? a. The volume of the large sphere is 4 times the volume of the smaller sphere b. The volume of the large sphere is 16 times the volume of the smaller sphere c.The volume of the large sphere is 12 times the volume of the smaller sphere d.The volume of the large sphere is 36 times the volume of the smaller sphere

semi circle

Any angle inscribed in a _____ is a right angle

They're congruent because they're intercepted by the same arc, and since they're similar from the AA congruence meaning that at least their angles will be congruent. 50.6 because 180 - (104.3+25.1)

How can we find out what angle E and C are? Solve EC

Final / Initial

How do you find the scale factor?

tan 21 = x/25 tan21 = y/25 tan21 times 25 9.596 tan40=z/25 tan40 times 25 20.977 20.977 -9.596 11.38

How long is the shadow? how?

1/2 the sum of the arcs, in this case PS and QR. PS+QR /2 = angles

How would you find Angle 1 and 2?

Since you have the intersecting angles for DFB, solve for that. (100.6) Now you have a linear pair, and when you solve you will get 79.4 (180-100.6)

How would you find CFD?

8 7²+x²=25² x²=576 x=24 (Remember the -4) x²+20²=25² x²=225 15-7=8

If the top of the ladder slips 4 feet, how many feet will the bottom slip? Explain.

CPCTC

If two triangles are congruent then all their corresponding parts are congruent. Used in a proof after showing triangles are congruent.

inscribed angles, intercepted arc

In a circle, 2 ________ angles with the same ________ are congruent

The length of the new aisle perpendicular to the hypotenuse coming from the right angle: n ... the new aisle n = a * b / c n = 47 * 110 / 119.62 n = 43.22 meters The correct result would be 43.22 meters

Read

d

Reflection over x axis a. (-x, -y) b. (-x, y) c. (y, -x) d. (x -y)

b

Reflection over y axis a. (-y, x) b. (-x, y) c. (x, -y) d. (x -y)

swaps the x and y coordinates and changes sign.

Reflection over y=-x

swaps the x and y coordinates.

Reflection over y=x

Opposite is across from the given angle Hypotenuse is across from 90 degree angle Adjacent is the non hypotenuse side Examples: https://imgur.com/a/BKw1WMY

Which side is the opposite side? Which side is the hypotenuse? Which side is the adjacent side?

E / C are the missing angle 50.6, which is inscribed so DB is double.

Why is DB 101.2?

5.66 / y = y / 5.66 y^2=32.0356 = 5.66

Solve

https://imgur.com/a/BEAh2wP

Solve

https://imgur.com/a/IdJ21l1

Solve

x (actual width of balcony) = 1 inch ----------------- -------- 84 inches (7 feet) 1.75 inches 1.75x=84 x= 4 feet perimeter 2(length+base) 2(7 feet+4 feet) 22 feet

Solve

TAN, because the opposite side is the tree since it's across from the angle you're finding. The adjacent is the shadow if the opposite side is where it is. it's atan(18/15) (O/A) = 50

Solve.

Exterior angles, because if you have the central angle it will be twice the size of the inscribed angle. Since B = D, B+D=2B.

Why would angle DAC be equal to D + B

104.3 Linear pair, then vertical angle

What belongs in the 2 circles? Why so?

when finding the ratio of the areas for scale factor, remember that you need to squareroot it to turn it into perimeter terms.

What do you need to remember when doing scale factor for area?

42 is an inscribed angle, meaning central angle R is 84. This make AH 84 as well. Since you have every side but AI, and since a circle has 360 degrees, you can now do 360-118-84 and get 158. Angle A is inscribed to 118, so you can do 118/2. to find H. Next find H by doing 180-59-42 (79) Now, H is inscribed to AI so simple multiply by 2 to get 158

What is AI, how would you find it? How would you find angle A and H?

22.5 Inscribed Angle

What is angle E? What IS angle E?

45 Central Angle

What is arc BC? Why so?

50, A is the central angle. 2x

What would DC equal if DAC was 50? What would DAC equal if DBC was "X"

I II IV

Which of the following can be formed when a plane intersects a cone? I. Circle II. Isosceles triangle III. Isosceles trapezoid IV. Parabola V. Rectangle VI.Square

a

Which of the following is correct? a.The sum of any 2 sides of a triangle must be greater than the measure of the third side. b.The sum of any 2 sides of a triangle must be less than the measure of the third side. c.The sum of any 2 sides of a triangle must be equal to the measure of the third side. d.The sum of any 2 sides of a triangle can be equal to the measure of the third side, but can also be greater.

ii iii v vi

Which of the following pairs of lines are perpendicular? i. y=2/3x+4 and y=2/3x-8 ii. y=2/3x-8 and y=-3/2x-8 iii. y=x+2 and y=-x+3 iv. y=3x+2 amd y=3x-2 v. y=3 and x=4 vi. y=4/5x-8 and y=-5/4x+3

c

Which of the following represents two lines that are coplanar and do not intersect? a. Perpendicular b. Skew c. Parallel d. Intersecting

II, III, V

Which of the following statements are correct? I. Only two of three angle bisectors of the internal angles of a triangle are concurrent II. The circumcenter of a triangle is the point where the perpendicular bisectors meet III. Given any three non-collinear points, there exists exactly one circle that passes through the points IV. A circumscribed Circle is the circle that passes through all three vertices of a triangle and it is the smallest triangle contained within any triangle. V. The incenter of a triangle is the point where the angle bisectors meet

All radii of the same circle are congruent, making 2 equal sides. They are radii because they come from the central point and touch a side of the circle. Angle B would be congruent to angle D, because the sides are congruent making the angles opposite congruent.

Why would triangle DAB be isosceles? What does that mean about the angles?

b

You are putting up a fence in your backyard to enclose a garden in the form of a triangle. The garden already has sides enclosed with eight feet and five feet of fence. What can you say about the length of the third side? a. The side needs a fence that is shorter than 8 ft but not necessarily longer than 5 ft. b. The side needs a fence that is longer than 3 ft and shorter than 13 ft c. The side needs exactly 8 ft. of fence. d. The side needs exactly 11 ft. of fence.

b

____, the sections made by planes ____ from their respective bases are always equal, then the volumes of the two solids are equal a. In two solids of equal width; parallel to and at the same distance b.In two solids of equal altitude; parallel to and at the same distance c.In two solids of equal width; perpendicular to and at the same distance d.In two solids of equal altitude; parallel to and at a proportional distance.