Geometry Flash Cards
dilation, reduction -> SF is .3 < 1
(x, y) ->(.3x, .3y)
Congruent, Scale Factor is 1
(x, y)->(x, y)
dilation, enlargement -> SF is 1.5 > 1
(x,y) -> (3/2 x, 3/2 y)
dilation, enlargement -> SF is 2 >1
(x,y)->(2x, 2y)
Pythagorean Theorem √a² + b² = c
*How do you calculate the distance?
corresponding angles are congruent
<2 & <6 <4 & <8 <1 & <5 <3 & <7
triangle angle sum = 180 nSolv, then multiply the answer by 2 for angle a and then by 3 for angle b
<a= 2x degrees <b= 3x degrees <c= 90 degrees What are the measurements of each angle?
nSolv (x, 2x and 3x=180,x)
A triangle has angles of x°, 2x° and 3x° What are the angles?
Area of the Base-use AREA on formula chart depending on the base
B in Volume means
Area of rectangle or parallelogram (l*w) or (b*h) or (s*s)
B of a volume of a cube
Area of rectangle or parallelogram (l*w) or (b*h)
B of of a volume of a rectangular prism
Area of a Circle-πr^2
B of volume of a cylinder
Area of a triangle-1/2 b h
B of volume of a triangular prism
Area of Base = circle -> πr^2*h
B=?
Volume= B x height of green or purple ( 5 x 8)(7)
Capacity
1/3 πr^2 h
Capacity of a cone
LSA = 2(green) + 2 (purple) 2(7x8) + 2 ( 7 x 5)
Cover sides of the box
hypotenuse of a right triangle
Diagonal, corner to corner, distance
2/3 πr^2 h
Fill a cylinder with 2/3 of sand
4/3 π r^3
Fill a sphere with air
Find c, then multiply by 4 to find the perimeter.
Find the perimeter of the 3rd square
Calculator nSolve( V = πr²h,h) or answer choices to substitute using formula V=πr²(h)
How do you solve for h?
B= area of circle = πr²
How would you calculate the area of the base?
Perimeter of the rectangle->add the length and width and multiply by 2
How would you find P of the shaded shape?
Calculator T or F or nSolve
Is the following a right triangle? lengths of 18 units, 24 units, 30 units
Calculator 1² + 1²= √2 T or F
Is this a right triangle?
area of rectangle S=2πrh
Lateral Surface area
Draw direction to use pythagorean theorem
North, East, South, West are used for what type of problems
Perimeter of Base-add the sides
P in lateral surface area mean
LSA = 2(green) + 2 (purple) 2(7x8) + 2 ( 7 x 5)
Paint 4 walls
Which of the following create a right triangle? 5, 13, 12 5, 4, 3 6, 8, 12
Pythagorean Theorem T or F on calculator
(X, Y) -> ( -Y, X) (3, 4) -> ( -4, 3)
ROTATION 90 DEGREES?
l= 8 w= 5 h= 7 2(lw) + 2(wh) + 2(lh) 2( 8x5) + 2 ( 5x7) x 2(8x7) 2(blue) + 2(purple) + 2 ( green)
TSA ☺
A= 1/2 b * h Nsolv(30=.5 * h, h)
The area of a triangle is 30 square inches, the base is 6.5, what is the height?
C= πd Nsolv(30 = π*d, d)
The circumference of a circle is 30 inches, what is the diameter?
C= 2πr nsolv(30 = 2 * π * r, r)
The circumference of a circle is 30 inches, what is the radius?
V = 4/3 π r^3 nsolv(30 = 4/3 * π *r ^3, r)
The volume of a sphere is 30 cubic units, what is the radius?
B = 1 blue ( lxw) (5x8)
Tile the floor
II
Top left quadrant
I
Top right quadrant
V=Bh = l*w*h nsolv(30 = 2 * 5 * h, h)
Volume of a rectangular prism is 30 cubic inches. The length is 2 and the width is 5, what is the height?
Net of a cylinder B = area of a circle, πr^2
What formula do I use for the B?
Total Surface Area of Triangular Prism - sum of area of rectangles (lxw) and triangle bases (1/2 bh) or Ph + 2B (P & B look like triangles)
What formula do you use to Wrap or Cover this shape?
Lateral Surface Area Triangular Prism- sum of the Area of the rectangles or Ph (P looks like a triangle)
What formula do you use to paint the walls of this shape?
B is area of base=rectangle l x w ->l =3ft w =6ft = 3x6=18 square feet
What is B =?
B is area of base=triangle 1/2 bh b = 3 ft h = 4ft 1/2 x 3ft x 4 ft = 6 square feet
What is B=?
P = Perimeter of base = rectangle = l + w + l + w l = 3ft w = 6 ft Perimeter = 3 + 6 + 3 + 6= 18 feet
What is P=?
P is the perimeter of the base = triangle a + b + c a= 3 ft b=4 ft c = 5 ft P = 3ft + 4ft +5 ft= 12 ft
What is P=?
B area of a rectangle
What is shaded?
B is a triangle = bh/2
What is the Area of the Base?
P is a triangle = s + s + s
What is the Perimeter of the Base?
Area of a rectangle is bh= 3 x 4 = 12 square units
What is the area of the base of a rectangular prism with a length of 3, width of 4 and height of 5?
side length if 3 -> 3 x 3 = 9 square units
What is the area of the smaller square?
A=bh/2 _____ x _____/2
What is the area of the triangle? Do you have all the dimensions needed?
Pythaogorean Theorem √3 squared + 4 squared = 5 units
What is the distance from B to C?
Distance, right triangle = pythagorean theorem
What is the distance from school to home?
Perimeter x SF, Area x SF x SF, Volume xSFxSFxSF Area of blue square 16 x SF x SF 16 x 1/4 x 1/4 = 1 square unit
What is the new area of the blue square if it has been dilated by a scale factor of 1/4?
Perimeter = l + w + l + w = 3 + 4 + 3 + 4 = 14 units
What is the perimeter of the base of a rectangular prism with a length of 3, width of 4 and height of 5?
side length is 3-> 3 + 3 + 3 + 3 = 12 units
What is the perimeter of the smaller square?
5 units
What is the side length of hypotenuse?
Scale Factor x side length .2 x 5 = 1unit SF .2 < 1 , side length will be smaller.
What is the side length of the hypotenuse if each side has been dilated by a scale factor of .2?
rise/run rise is 10 run is 15 = 10/15 = 2/3
What is the slope?
.25(15)= .25(10)=
What scale factor would reduce each length by 1/4?
Dilation
Which transformation does not preserve congruence?
TSA = 2(green) + 2(purple) + 2 (blue) 2(7x8) + 2 ( 7 x 5) + 2( 5 x 8)
Wrap a gift, which do I use?
IV
bottom right quadrant
vertical angles
congruent angles across each other form v's horizontally and vertically
alternate interior angles are congruent
inside angles form a capital i angles are diagonal from each other <3 & <6 <4 & <5
alternate exterior angles are congruent
outside angles form a letter z <2 & <7 <1 & <8
3 and 4
π is between which two numbers on a numberline
