# Geometry

### Featured Answers

### Angles and Intersecting Lines

- Angle Basics and Measurements
- Angles Between Intersecting and Parallel Lines
- Complementary and Supplementary Angles
- Angles with Triangles and Polygons
- Perpendicular Bisectors
- Angle Bisectors
- Altitudes
- Medians and Centroids
- Quadrilaterals
- Dilations or Scaling around a Point
- Properties and Definitions of Transformations
- Rotations
- Reflections
- Rigid Transformations
- Transformations and Congruence
- Triangle Congruence
- Theorems concerning Triangle Properties
- Theorems concerning Quadrilateral Properties
- Proofs
- Triangle Similarity
- Solving Similar Triangles
- Angle Bisector Theorem
- Solving Problems with Similar and Congruent Triangles
- Solving Modeling Problems with Similar and Congruent Triangles
- Circle Arcs and Sectors
- Central, Inscribed, and Circumscribed Angles
- Equation of a Circle
- Area of Inscribed Triangle
- Pythagorean Theorem
- Pythagorean Theorem Proofs
- Special Right Triangles
- Sine, Cosine and Tangent Functions
- Trig Ratios and Similarity
- Perimeter and Area of Triangle
- Triangle Inequality Theorem
- Heron's Formula
- Circumference and Area of Circles
- Perimeter and Area of Non-Standard Shapes
- Volume of Solids
- Geometry Problems on a Coordinate Plane
- Distance between Points
- Equations of Parallel and Perpendicular Lines
- Constructing Bisectors of Lines and Angles
- Constructing Regular Polygons Inscribed in Circles
- Constructing Circumcircles and Incircles
- Constructing a Line Tangent to a Circle
- Find the length of the tangents from the origin to tge circle #3x²+3y²+12x+8y+8=0#. Find also the acute angle between the tangents from the origin to the circle (answer#= (2*sqrt6)/3 ,86°#)?
- If the surface area of the earth is 510,460,000 km^2, what is the radius of the earth in meters?
- How is the area of a wall calculated?
- Who is considered the father of geometry?
- The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The area of the resulting rectangle is #90 ft^2#. What is the original area of the square?
- A storage container is 22 inches long. 22 inches wide, and 24 inches deep. What is the volume of the container?
- There is a rectangle with width #4x# and height #(7/3)x#. What is the area of the rectangle when #x = 6#?
- How is the number of sides related to the sum of the interior angles in a polygon, and what about the sum of the exterior angles?
- What is the total number of diagonals for a hexagon and a heptagon?
- What is the area of a circle with an 8 cm diameter, in terms of #pi#?
- A rectangular box has two sides whose lengths are 3 centimeters and 9 centimeters and a volume of 135 #cm^3#. What is the area of its largest side?
- If the sector formed by a central angle of 30° has an area of #pi/3# square centimeters, what is the radius of the circle?
- A garden measures 17 meters by 24 meters. What is the area of the garden, and how much fencing is needed to enclose the garden?
- What is the perimeter of the rectangle with sides 5#1/3# in and 10#1/6#in?
- How many #2 1/2# acre plots can be made out of a #35# acre plot?
- The points #(n-2, n - 3)#, #(n + 1, n+9)# , and #(70, n -31)# are collinear. What is the value of #n#?
- The ﬁrst Ferris wheel, designed by George Ferris was built in 1893 in Paris. France. It had a diameter of 76 m. About how far would you travel in 8 turns of this wheel?
- A land mass is roughly in the shape of a rectangle whose perimeter is 1100 miles. The width is 110 miles less then the length. What is the width?
- What is the width of a rectangular prism when the surface area is 208 square centimeters, and it has a height of 8 and a depth of 6?
- What is the circumference of a circle with a radius 24 m in terms of #pi#?
- You have a container whose box whose volume is 216 cubic centimeters. If your container is a cube, what is the length of each of its dimensions?
- A rectangle has an area of #17.6# #m^2#. lf the width is #2.3# meters shorter than the length, what are the dimensions of the rectangle?
- If AB = 6, BC = 4, and AE = 9, what is ED?
- A bulletin bound is 56 m. wide and 36 in. high. How many 3#1/2# in. columns can be created?
- A triangle with side lengths 5, 11, and 15 is similar to another triangle with longest side of 24. What is the perimeter of the larger triangle?
- What is the measure of each exterior angle in a regular dodecahedron?
- The length of a rectangular pool is 2 feet less than twice the width. If the area of the poet is 264 f#t^2#. What are the dimensions of the pool?
- What is the perimeter and area of a rectangle with sides 22 and 16?
- Triangle ABC have vertices #A(0,4)#, #B(1,2)#, and #C(4,6)#. Is triangle ABC a right triangle?
- Why do we say a rectangle is a special case of a parallelogram?
- A kitchen ﬂoor has 15#1/2# tiles in an area of 2#3/5# square feet. How many tiles are in one square foot?
- Two angles are complementary. lf the measure of one angle is 20 more than the measure of the second angle, what is the number of degrees in the measure of the smaller angle?
- A rectangle has a perimeter of 70 centimeters and a length of 21 centimeters. What is its width?
- The area of the ﬂoor in a rectangular kitchen is 209,196 square centimeters. The area of each square tile is 36 square centimeters. How many square tiles are needed to tile the kitchen ﬂoor?
- What is the sum of the measures of the interior angles of a 28-gon?
- The area of the gym ﬂoor is 6,536 square feet. The length of the ﬂoor is 76 feet. What is the width?
- What is the circumference of a circle with a radius of 4 inches?
- A sugar cube has a volume of 0.216 cubic inches. What is the length of each edge?
- If the area of a square is 29 square inches, what is the length of each side of the square?
- What is the width of a rectangle if its perimeter is 216 centimeters and its width is 24 centimeters less than its length?
- What is the length of a rectangle if its perimeter is 279 feet and its length is 2.1 times its width?
- What is the length of the diagonal of a rectangle with a length of 6 in. and a width of 4 in.?
- A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower?
- The coordinates of the endpoints of the diameter of a circle are #(3, 8)# and #(-7, 2)#. What are the coordinates of the center of the circle?
- A rectangular solid has a surface area of #22 cm^2# and a volume of #6 cm^3#. What is the surface-area-to-volume ratio?
- If two polygons are similar, how can you find the scale factor from one polygon to the other?
- The radius of a circular garden pond is 1.75 feet. What is the diameter of the pond?
- What is the width of a rectangular prism if the volume = #80# #i##n^3#, the height is #2# #i##n#, and the length is #8# #i##n#?
- Is a rhombus always a trapezoid?
- How do you find the area of a trapezoid when you have the length of every side but not the height?
- What are at least 2 characteristics of a rhombus?
- A rhombus has sides of 5 inches in length, two 60 degree angles, and two 120 degree angles. What is its area?
- A rhombus has a side of 12 and the measure of one angle is 150 degrees. What is its area?
- What is the perimeter of a rhombus with diagonals 10 and 24?
- A bicycle wheel travels about 82 inches in 1 full rotation. What is the diameter of the wheel?
- The congruent sides of an isosceles triangle are 13 cm. If its height is 12 cm, what is the length of the base of the isosceles triangle?
- ABC is an isosceles triangle with angle B = angle C. Point P is the midpoint of AB. If angle A is 30 degrees, what is angle PCB?
- How many sides does a tetrahedron have?
- In rhombus #ABCD#, the length, in inches of #AB# is #3x + 2# and #BC# is #x + 12#. Wha tis the number of inches in the length of #DC#?
- Question #ccd69
- Question #179ea
- Does #pi^2# have any physical meaning?
- A rectangular box has a length of 8 feet and a width of 2 feet. The length of the three-dimensional diagonal is 10 feet. What is the height of the box?
- A square has sides of length #s#. A rectangle is #6# inches shorter than the square and #1# inch longer. How do you write an expression to represent the perimeter of the rectangle?
- If the perimeter of a rectangle is 56 cm and the width is 13 cm, what is the length?
- A wheel on Donna's bicyde is 0.3 min diameter. Donna races the bicycle for 39 m. How many times does the wheel turn as the bicycle travels this distance?
- What is the area of a triangle when #b = 12# inches and #h = 7# inches?
- The equation #P = 3s# represents the perimeter #P# of an equilateral triangle with side length #s#. What is the perimeter of an equilateral triangle with side length #4# #ft#?
- What is the area of an isosceles right triangle with hypotenuse #6sqrt2#?
- What is the length of the hypotenuse of a 45-45-90 triangle, if its leg is x units long?
- What is a dilation, or scaling around a point?
- Mrs. Smith wants a circular patio with a diameter of 12 feet and Mr. Smith wants a square patio with a side of 12 feet. Which would have a larger area and by how much?
- An equilateral triangle is inscribed in a circle of radius #6x#. What is the area #A# within the circle but outside the triangle as a function of the length #9x# of the side of the triangle?
- A triangle is dilated using a scale factor of 4. The image is then dilated using a scale factor of 3. What scale factor could you use to dilate the original triangle to get the final image?
- How many degrees are in a triangle?
- What is the name of the point that is two-thirds of the way from each vertex of a triangle to the midpoint of the opposite side?
- What is the point called where the perpendicular bisectors of the sides of a triangle intersect?
- If a circle with a diameter of 4 inches rotates 1000°, what distance will any one spot on its edge actually travel?
- A four sided figure has a perimeter of 26. The other three sides' measurements are 10.5, 9, and 2.8. What is the measure of the last side?
- Mr. Sprout built a fence around his garden so it formed a square with ten fence posts on each side. How many fence posts did he need?
- A right triangle is formed by the origin and the x- and y-intercepts of the line #11x - 4y = 22#. What is the area of the triangle?
- If the radius of a circle is double, how is the length of the arc intercepted by a fixed central angle changed?
- The surface area of a Rubik's cube is 54 sq in. What are the dimensions of each face?
- A cube has a volume of 125 cubic feet. What is the length of each edge?
- What is the definition of a circle?
- The perimeter of a rectangle is 82 m. If the width were doubled and the length were increased by 18 m, the perimeter would be 150 m. What are the length and width of the rectangle?
- A small square window has an area of 36 square inches. What is the length of each side?
- The length of a rectangle is 9 cm less than 4 times the width. The perimeter is 142 cm. What is the width and length?
- Equation of circle passing through (-1,-2) and concentric with the circle x^2 +y^2 +3x + 4y +1 =0 ?
- A rectangle is #6# units wide and #x-8# units long. It has the same area as a triangle with a height of #7# units and a base of #x-3# units. What is the area of the rectangle?
- What is locus?
- A regular polygon has interior angles that are 5 times larger than each of its exterior angles. How many sides does the polygon have?
- A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4 m. The length of the rectangular carpet is 2 m less than three times its width. What are the dimensions of the rectangular carpet?
- The Canadian $1 coin has 11 equal sides. The perimeter is 7.7 cm. How long is each side?
- The perimeter of a square is 4 times as great as the length of any of its sides. Is the perimeter of a square proportional to its side length?
- Triangle #JAR# has vertices #J(1,4), A(3,5)# and #R(2,1)#. If you reflect triangle #JAR# across the #y#-axis, what will the coordinates of the vertices of the image triangle #J'A'R'# be?
- What is #x# if the perimeter of a rectangle with sides of #x# and #2x + 6# is #27# in?
- The perimeter of a hexagonal park is 852 km. How long is each side of the park?
- A person makes a triangular garden. The longest side of the triangular section is 7 feet shorter than twice the shortest side. The third side is 3 foot longer than the shortest side. The perimeter is 60 feet. How long is each side?
- What is the area of a rectangle with sides 7 and 13?