Geometry Part 1
Centroid
The ___ is the center of gravity or balancing point of a triangle.
Circumcenter
The ___ of a right triangle is located on the hypotenuse.
Orthocenter
The ___ of a right triangle is located on the right angle.
Median
The line segment joining a vertex to the midpoint of the opposite side is the ___.
perpendicular bisector
The line segment that is both perpendicular to a side of a triangle and passes through its midpoint is the ___.
14 cm
The prism shown has a volume of 3,024 cm3. What is the height of the prism? 7 cm 14 cm 21 cm 30 cm
4 cm
The prism shown has a volume of 77 cm3. What is the width of the prism? 2 cm 4 cm 22 cm 33 cm
10.5 cm
The prism shown has a volume of 798 cm3. What is the height of the prism? 8.6 cm 10.5 cm 17.5 cm 45.6 cm
Angle Bisector
The segment drawn from a vertex that bisects that angle is the ___.
Altitude
The segment that makes a right angle and goes through the vertex is the ___.
Orthocenter
The three altitudes of a triangle intersect at the
Incenter
The three angle bisectors of a triangle intersect at the
Centroid
The three medians of a triangle intersect at the
Circumcenter
The three perpendicular bisectors of a triangle intersect at the
Centroid
The triangle center shown is the ___.
Circumcenter
The triangle center shown is the ___.
Incenter
The triangle center shown is the ___.
Orthocenter
The triangle center shown is the ___.
14 161
Use the formula V = Bh to calculate the volume of this prism. The area of the base, B, is ___ in.2. The volume of the prism is ___ in.3.
148.5 m cubed
What is the volume of the rectangular prism? 16 m3 33 m3 148.5 m3 181.5 m3
267.75 mm cubed
What is the volume of the rectangular prism? 21 mm3 76.5 mm3 80 mm3 267.75 mm3
V = Bh V = lwh
Which formulas can you use to calculate the volume of a rectangular prism? Check all that apply. V=1/2bh V = 2l + 2w V = Bh V = lw V = lwh V = s2
6*3*2 3/4=49 1/2 cm cubed
Which is the correct calculation for the volume of the prism?
2 1/2*8*8 1/2=170mm cubed
Which is the correct calculation for the volume of the prism? 2 1/2+8+8 1/2=19mm3 2 1/2 *8+8 1/2=28.5mm3 8*8 1/2=68mm3 2 1/2*8*8 1/2=170mm3
Orthocenter and Circumcenter
Which two points of concurrency are always located outside of an obtuse triangle?
Density Equation
d= m/v
What is the volume of a sugar cube that measures 1 cm on each side?
1 cubic centimeter
A cylindrical water tower is half full of water. How many cubic feet of water are in the tower if it measures 20 feet high and has a radius of 7 feet? Use 3.14 for pi.
1,538.6 cubic feet
A rock has a mass of 77.0 grams. The volume is found using water displacement. The initial volume of water is 10.0 mL and the volume of the rock and water is 17.0 mL. Determine the rock's density
11.0 grams/cm^3
What is the volume of a storage area measuring 5 feet on each side?
125 cubic feet
What is the total volume of an object that had an initial volume of 30 mL and a final volume of 45 mL?
15 mL
Find the mass of a piece of gold that has a volume of 3.0 cm^3. The density of gold is 6.0 g/cm^3.
18.0 g
A pile of gravel is in the shape of a cone. If the pile is 8 feet high, and the diameter of the pile is 10 feet, how many cubic feet of gravel are in the pile?
209.3 cubic feet
How many cubic yards of sand will it take to fill a child's play area that measures 10 yards long, 8 yards wide, and 1/3 yard deep?
26 2/3 cubic yards
A pile of sand is shaped like a cone. If the height of the pile is 7 meters and the radius of the pile is 6 meters, how many cubic meters of sand are in the pile?
263.76 cubic meters
The mass of a chocolate bar is 10g, the density of the chocolate bar is 3g/cm cubed. What is the volume of the chocolate bar? (round to the nearest hundredth if necessary.)
3.33cm cubed
. The object's dimensions are 10.0 cm x 2.0 cm x 2.0 cm. Calculate the object's volume.
40 cm^3
How many cubic feet of concrete will be needed for a driveway section that is 10 ft long, 8 feet wide, and 1/2 foot thick.
40 cubic feet
What is the volume of a wooden block that is 45cm by 2cm by 0.5cm
45cm cubed
How many cubic yards of topsoil are needed to put in a lawn if the lot measures 50 feet by 80 feet and the topsoil is to be 1/3 foot thick? Hint: Do all work in feet and then convert to yards. 3 feet= 1 yard
49.4 cubic yards
A glass is 7 inches high and has a diameter of 3 inches. How many cubic inches of water can the glass hold when filled to the top?
49.5 cubic inches
A bronze block has a mass of 56g and a volume of 14cm cubed, what is the density?
4g/cm cubed
A cylindrical oil drum is 2.1 meters high and has a radius of 0.9 meters. How many cubic meters of oil can the drum hold? Round to the nearest whole number
5 cubic meters
An object has a mass of 100.0 grams. The object's volume is 20.0 cubic centimeters. What is the object's density
5.0 grams/cm^3
What is the total volume of an object that had an initial volume of 20 mL and a final volume of 27 mL?
7 mL
The volume of an iron block that is 4cm by 6cm by 3cm is:
72cm cubed
Perpendicular Bisector
A line that is perpendicular to a segment at its midpoint.
Angle Bisector
A line, segment, or ray that divides an angle into two congruent, adjacent angles.
Altitude
A perpendicular segment from a vertex to the line containing the opposite side. Otherwise known as height.
Circumcenter
A point of intersection formed by perpendicular bisectors of the sides of a triangle. It is equidistant from all three vertices.
Incenter
A point that is equidistant from the three sides of the triangle and is formed by the intersection of angle bisectors.
v=lwh 238=l*8 1/2*3 1/2
A prism has a volume of 238 cubic millimeters Which is the correct substitution for finding the length of the prism?
112.5 cm cubed
A rectangular prism has a length of 4.5 cm, a width of 10 cm, and a height of 2.5 cm. What is the volume of the prism? 11.25 cm3 17 cm3 112.5 cm3 1,125 cm3
length of 1 ft; width of 81 ft
A square storage unit has a volume of 607.5 ft3. The height of the unit is 7.5 ft. What are the length and width of the storage unit? length of 1 ft; width of 81 ft length of 2 ft; width of 40.5 ft length of 3 ft; width of 27 ft length of 9 ft; width of 9 ft
64 8 8
A storage unit that has a square base has a volume of 480 ft3. The height of the unit is 7.5 feet. prism What is the area of the square base? The area of the square base is ____ feet2. What is the length and width of the storage unit? The length of the unit is ___ feet. The width of the unit is ____ feet.
l=210/5 ft
Asher began working through the problem using the steps. His work is shown. 1. Write the formula. V = lwh 2. Substitute for the known values. 210 = l(3)(5) prism A prism has a width of 3 feet, a height of 5 feet, and a volume of 210 ft3. Which equation shows the length of the rectangular prism? l=(210/3)5 l=210/5 l=210(15) l=(210/3)3
M = 48g, V = 8cm3 D = ?
D = 6 g/cm3
Altitude
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Angle Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Median
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Perpendicular Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Centroid
It divides each median into two sections at a 2:1 ratio.
Incenter
It is equidistant from the three sides of a triangle.
Circumcenter
It is equidistant from the three vertices of a triangle.
Orthocenter
It is the point in a triangle where the altitudes of the triangle intersect.
D = 7g/cm3, V = 3 cm3 m = ?
M = 21 g
Square
Parallelogram with: Both pairs of opposite angles are congruent to each other Diagonals are perpendicular
Parallelogram
Quadrilateral with: 2 pairs of opposite sides parallel opposite angles are congruent opposite sides are congruent 2 consecutive angles are supplementary
x = 9
Solve for x if the given quadrilateral is a rectangle
x = 20
Solve for x if the given quadrilateral is a rhombus
x = 8
Solve for x if the given quadrilateral is a rhombus
x = 10
Solve for x if the given quadrilateral is a square
He multiplied the denominators incorrectly
Tanner calculates the volume of a rectangular prism with dimensions 3/4 ft by 5 ft by 1/2 ft. His work is shown below. What error did Tanner make? He multiplied the numerators incorrectly. He multiplied the denominators incorrectly. He simplified 15/6 incorrectly. He wrote 5 as a fraction incorrectly.
