Angles and Intersecting Lines
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Angle Basics and Measurements
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Angles Between Intersecting and Parallel Lines
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Complementary and Supplementary Angles
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Angles with Triangles and Polygons
Special Properties and Parts of Triangles
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Perpendicular Bisectors
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Angle Bisectors
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Altitudes
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Medians and Centroids
Quadrilaterals
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Quadrilaterals
Transformations
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Dilations or Scaling around a Point
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Properties and Definitions of Transformations
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Rotations
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Reflections
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Rigid Transformations
Congruence
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Transformations and Congruence
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Triangle Congruence
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Theorems concerning Triangle Properties
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Theorems concerning Quadrilateral Properties
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Proofs
Similarity
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Triangle Similarity
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Solving Similar Triangles
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Angle Bisector Theorem
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Solving Problems with Similar and Congruent Triangles
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Solving Modeling Problems with Similar and Congruent Triangles
Circles
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Circle Arcs and Sectors
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Central, Inscribed, and Circumscribed Angles
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Equation of a Circle
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Area of Inscribed Triangle
Right Triangles and Trig
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Pythagorean Theorem
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Pythagorean Theorem Proofs
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Special Right Triangles
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Sine, Cosine and Tangent Functions
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Trig Ratios and Similarity
Perimeter, Area, and Volume
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Perimeter and Area of Triangle
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Triangle Inequality Theorem
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Heron's Formula
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Circumference and Area of Circles
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Perimeter and Area of Non-Standard Shapes
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Volume of Solids
Analytic Geometry
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Geometry Problems on a Coordinate Plane
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Distance between Points
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Equations of Parallel and Perpendicular Lines
Geometric Constructions
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Constructing Bisectors of Lines and Angles
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Constructing Regular Polygons Inscribed in Circles
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Constructing Circumcircles and Incircles
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Constructing a Line Tangent to a Circle
Uncategorized Questions
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A rectangle has sides of #(7 + sqrt2)# feet and #(7 - sqrt2)# feet long. What is the area and the perimeter of the rectangle?
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A copper wire when bent in the form of a square encloses an area of #121##cm^2#. If the same wire is bent into the form of a circle, what is the area of the circle?
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The vertices of triangle #XYZ# are #X(0,0), Y(0,7),# and #Z(6,3)#. What are the coordinates of the orthocenter of triangle #XYZ#?
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Directed line segment AB has endpoints #A(4, 8)# and #B(4, 4)#. What are the coordinates of the point that will partition the segment into a 3:1 ratio?
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What is the sum of interior angles of a 34-gon?
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What is the measure of one interior angle of a regular nonagon?
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A rectangle is inscribed in an equilateral triangle, with one side on a side of the triangle. If the triangle has side of length 2, what is the maximum possible area of the rectangle?
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If you split an equilateral triangle as it sits on its base horizontally, at what height would the top and bottom areas be equal? Using variables?
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The width of a rectangle is 15 centimeters. If the perimeter of the rectangle is 86 centimeters, what is the length?
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The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool?
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Nathan plants equal-sized squares of sod in his front yard. Each square has an area of 6 square feet. Nathan plants a tota| of 1,000 squares in his yard. What is the total area of the squares of sod?
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A landscape architect is planning a new nature area in the middle of a campus.She wants the length to be twice the width, and wants to put a 3-foot high retaining wall around the perimeter. There will be 300 total feet of wall. How wide will this area be?
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What is #n# if each interior angle of a regular #n#-gon measures 172.8°?
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What is the measure of an exterior angle of a dodecagon?
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Question #0d0b8
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Three interior angIes of a quadrilateral have measures of 111°, 134°, and 69°. What is the fourth angle measure?
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Marie has a small copy of Rene Magritte's famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in:40 cm. What is the dimensions of the original painting?
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What is the perimeter and area of a rectangle with width 5 centimeters and length 16 centimeters?
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What is the area of a triangle with base 13 ft. and height 6 ft.?
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What is the perimeter and area of a square with a 12 ft. side.?
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What is the area of a parallelogram with height 6 inches and base 11 inches?
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One side of a triangle is 5 meters longer than the second side. The third side is four times the length of the second side. If the perimeter of the triangle is 65 meters, how long is the second side?
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Ten times the perimeter of a square is 360 yards. What is the length of each side of the square?
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The height of a triangle is 18 inches. What is the length of the base if the area of the triangle is 63 square inches?
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Twice the area of a square is 72 square miles. What is the length of each side of the square?
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The length of a rectangle is three times the width. What is the width of the area is 147 square feet?
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One angle of a triangle measures 12 degrees. The second angle's measurement is five times the third. What is the measure of the third angle?
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The height of a triangle is four times the length of the base. What is the base and height of the triangle if the area is 18 square inches?
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The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?
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One angle of a triangle is 20 degrees. The second angle's measurement is four times the third. What is the measure of the third angle?
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The width of a rectangle is 6 centimeters less than the length. The perimeter is 64 centimeters. What is the width?
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Two angles of a triangle are 40 degrees and 62 degrees; what is the third angle's measure?
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A rectangular prism has dimension of .5 feet, 4 inches, and 2 inches. How much volume does the digital camera occupy, in inches?
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A box of milk powder has a length of 12 centimeter, a width of 6 centimeter and a height of 70 millimeters. What is the volume of milk powder it holds, in centimeters?
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Question #ba50a
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The lengths of the tangents from any point on the circle #15x^2 + 15y^2 -48x +64 y =0# to the two circles #5x^2 + 5y^2 -24x +32y +75 =0# and #5x^2 + 5y^2 -48x +64y +300 =0# are in the ratio?
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The number of real tangents that can be drawn from (2,2) to the circle x^2 + y^2 -6x -4y +3 =0 ?
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Product of slopes of two perpendicular lines is -1. Slope of x-axis is 0 and that of y-axis is ∞. So , how can be the product of 0 and ∞ equals -1?
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Question #8d215
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An arc has a length of 25 in. The radius of the circle is 8 in. What is the degree measure of the arc?
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The length of a rectangular field is 24 meters. This is 3 meters less than twice the width. What is the width?
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The base of a triangle is twelve more than twice its height. If the area of triangle is 53 square centimeters, what is its base and height?
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A sphere has a volume of #288pi#. What is the radius?
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If the volume of a cylinder is #441pi# #cm^3# and has a radius of #7# #cm#, what is the height of the cylinder?
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What is the measure of one interior angle in a pentagon?
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What is the measure of one interior angle in a octagon?
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The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an obtuse angle of the parallelogram?
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A funnel that is used to change the oil in a car is in the shape of a cone. The base of the funnel has a circumference of 60 centimeters. The height of the funnel is 25 centimeters. How much oil will this funnel hold?
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In triangle abc, what is the length of side a to the nearest whole number of side b = 20, angle A = 43° and angle C = 72°?
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An escalator at a shopping center is 200 ft 9 in. long, and rises at angle of 15°. What is the vertical rise of the escalator?
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Is there a unit smaller than a second in the sexagesimal measure of angles system? Thanks:)
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Frances wants to fence in a 6' by 8' tomato garden. Will 30' of fencing be enough?
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The interior angles of a triangle are #(x+10)°#, #(3x)°#, and #(2x+30)°#. What is the value of #x#?
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There is a cylindrical fish tank with a radius of 10 and a height of 3. Your fish need a tank with a volume of at least 900 cubic units; will this tank work for you fish?
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A square rug has a perimeter of 36 ft. What is the length of each edge of the rug?
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What is the area of a trapezoid with one base of 26 cm, another case of 28 cm, and a height of 14 cm?
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Show that apothem of the equilateral triangle, of which one side length is a, will be #sqrt3/6a#?
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A rectangular picture frame has a perimeter of 58 inches. The height of the frame is 18 inches. What is the width of the frame?
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Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 feet from camera 2, which was 121 feet from camera 3. Cameras 1 and 3 were 140 feet apart. What camera had to cover the greatest angle?
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#/_A# and #/_B# are complementary. #m/_A = (5x+2)°#. What is #m/_B#?
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The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?
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The area of a rectangle is #5 4/5# square meters. The width of the rectangle is #2 1/4# meter. How long is the rectangle?
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The bulletin board is 6 feet wide and 4 feet tall. The border is 3 inches wide. What are the dimensions inside the border?
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A rectangular pen is made with 180 meters of fencing on three sides. The fourth side is a stone wall. What is the greatest possible area of such an enclosure?
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Hakeem's front porch measures #9 3/4# feet by #4# feet What is the area of his front porch?
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The vertices of a trapezoid are #A(1, 1), B(2, 2), C(4, 2),# and #D(5, 1)#. If you rotate the trapezoid 90° clockwise about the origin, what are the new coordinates?
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 420 feet. What is the flag's length and width if the length is 110 feet greater than the width?
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What is the circumference of a circle whose radius is 7 centimeters?
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A triangle has angles of #7x + 10, x + 20,# and #2x#. What is the measure of the largest angle?
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The perimeter of a rectangle is 148 feet. The length is 14 ft, greater than one and a half times the width? What is the length of the rectangle?
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One angle of a triangle is 3 times as large as another. The third angle is twice the sum of the first two angles. What is the measure of the largest angle?
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The perimeter of a rectangle is 42 cm. The length is 3 cm greater than the width. What is the length?
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The perimeter of a triangle is 79.75 inches. The second side of the triangle is half as big as the first side. The third side is 7.25 in. greater than the first side. What is the length of the longest side of the triangle?
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Where can the perpendicular bisectors of the sides of a right triangle intersect?
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What is the area of a trapezoid that has a base of 8 in, another base of 13 in, and a height of 5 in?
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What is the sum of all interior angles of a regular heptagon?
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What is the range of measure of the third side of a triangle that has sides of 5 ft and 7 ft?
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What is the range of measure of the third side of a triangle that has sides of 10.5 cm and 4 cm?
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The perimeter of a football field rink is 346 yards. If the length is 14 yards more than 2 times the width, what are the dimensions?
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Each of the equal sides of an isosceles triangle is 4 times the third side. The perimeter of the triangle is 117 inches. What are the sides of the triangle?
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Question #6e48a
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The length of a rectangle is 8 in. more than its width. The perimeter of the rectangle is 24 in. What are the width and length of the rectangle?
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#JKLM# is a rhombus. If #m/_JML = 70°#, what is the value of #m/_JKM#?
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Two angles are complementary. If #m/_ 1 = (3x)°# and #m/_2 = (6x)°#, what is #x#?
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#m/_ABC = 39°#. What is its supplement and complement?
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Triangle #ABC# has vertices #A(-2, 1), B (-4, -1), #and #C(0,-1)# and is reflected in the line #x=2#. What is the coordinate of C'?
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A rectangle has a height of #2x+5# and a width of #3x-5#. What is the perimeter of the rectangle?
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A flagpole 8.2 meters tall casts a horizontal shadow 4.0 meters long. What time is it if the sun was directly overhead at 12:10 pm and will set at 6:10 pm?
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Why can't you prove triangles congruent by using side-side-angle?
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Base of an isosceles triangle #XYZ# is #XZ# and coordinates of its vertices are mentioned as #X(-2,3),Y(1,5)# and #Z(square,2)#. What is the missing coordinate?
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How do you draw a regular hexagon with a ruler and compass?
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Let side lengths of a triangle be #a#, #b#, and #c#. Then how do you proof that #a^2<2(b^2+c^2)#?
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Carmen measures a room to be #10# #1/2# feet by #12# #5/8# feet. What is the area of the room written as a decimal?
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The measures of the three angles of a triangle are given by #18x-7, 12x + 9#, and #4x#. What is the measure of the largest angle?
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What is the height of a cylinder with a volume of #720pi# #ft^3# and radius of #6# #ft#?
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Point (-3, 4) is rotated 180° about the origin in a counterclockwise direction. What are the coordinates of its image?
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A stop sign has the shape of a regular octagon. What is the sum of the interior angles of a stop sign?
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Triangle #ABC# has vertices #A(-2,1), B(-4,-1),# and #C(0, -1)# and is reflected in the line #x = 2.# What is the coordinate of #C'#?
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A rectangular field measures 325 m by 240 m. How much shorter would it be to walk diagonally across the field than to walk around two sides of the field?
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The perimeter of a rectangle is 36 meters. The length of the rectangle is 4 meters longer than the width. What is the length and width of the rectangle?