 3D Vision  Annie Fetter
PreAlgebra, difficulty level 3. When you fold up the given net of a cube, what shape is formed by the segments on the faces of the cube?
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 Added Areas  Annie Fetter
Geometry, difficulty level 1. A circle and an isosceles triangle are inscribed in a square. If the areas of the three figures added together is 28 square units, what's the edgelength of the square?
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 Aim at This Target!  Annie Fetter
Geometry, difficulty level 4. Figure out the areas of different parts of this target, and the relation between the different areas. Can you explain this relation?
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 All Around the World  Terry Trotter & Annie Fetter
Geometry, difficulty level 2. If a wire wrapped around the equator of the Earth is lengthened by 100 meters, how far above the surface of the Earth would the wire now be if lifted off the surface an equal distance all the way around?
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 Angle Trisection with a Carpenter's Square  Annie Fetter
Geometry, difficulty level 3. Prove how a carpenter's square can be used to trisect an angle.
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 Another Ambiguous Angle?  Annie Fetter
Geometry, difficulty level 3. Given isosceles triangle ABC, with BE perpendicular to AD. If angle ACB is x, what is angle CBE?
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 The Apprehendable Angle  Annie Fetter
Geometry, difficulty level 2. Triangle ABC is isosceles with a vertex angle (at the top) of 50 degrees. If D is on AC, E is on BC, and AD = BE, what is the measure of angle ADE?
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 Approximating the Circumference and Area of a Circle  Annie Fetter
Geometry, difficulty level 2. Take a circle and circumscribe a square and inscribe a square. Construct a square between the other two squares, and compare the area and the perimeter of the middle square with the area and circumference of the circle.
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 Arc to Area  Annie Fetter
Geometry, difficulty level 4. Given an arc with a measure of 40 degrees whose endpoints are at (1,5) and (5,3), find the area of the circle that contains the arc.
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 Area of a Rectangle  Annie Fetter
Geometry, difficulty level 2. Given rectangle ABCD with point E on CD. AE is 3, BE is 4, and AE is perpendicular to BE. What's the area of ABCD?
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 Areas of Circles in a Target  Annie Fetter
Geometry, difficulty level 2. Given one circle inside another circle. If the outer circle is 36 inches in diameter, how big must the inner circle be so that the area of the inner circle equals the area of the outer circle NOT covered by the inner circle?
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 Arranging Six Squares  Annie Fetter
Geometry, difficulty level 3. How many ways can you arrange six squares in the plane so that they all share an edge with at least one other square? How many of these configurations could be folded up to form a cube?
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 As Far as the Eye Can See  Annie Fetter
Geometry, difficulty level 4. If I'm 5'10" tall, can I see the entire length of Lake Memphramagog, which is about 23 miles long?
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 Building a Bridge Across a Chasm  Annie Fetter
Geometry, difficulty level 2. So they're standing on the edge of this chasm. It isn't really that far across, but they need to find a log or tie together enough rope to reach a tree on the other side. So they mark a spot on the edge of the chasm directly
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 Building a Dog Enclosure  Annie Fetter
Geometry, difficulty level 3. Two people are arguing about whether three sections of fencing 6, 8, and 10 feet long will enclose more or less area than three sections 6, 8, and 12 feet long.
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 Building a Rain Gauge  Annie Fetter
Geometry, difficulty level 3. Given the depth of the water in a bottle, figure out how much rain really fell, considering that the opening of the bottle is much smaller than the main part.
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 Building a Snow Statue  Judy Ann Brown
PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
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 Building a Vaulted Ceiling  Annie Fetter
Geometry, difficulty level 4. An eyebrow window is a 15inchdeep slice off an 8.5foot circle. How wide will the base of the window be?
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 Building Fences  Judy Ann Brown
PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
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 Building Polygons  Annie Fetter
Geometry, difficulty level 2. Put squares on the edges of an equilateral triangle and connect their outside corners to form a hexagon. Do the same thing with a regular hexagon. Are the resulting figures equilateral? Are they equiangular?
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 Build Your Own Hexagon  Annie Fetter
Geometry, difficulty level 2. Put a square on each edge of an equilateral triangle (edgelength one unit) and connect the outside vertices of adjacent squares to form a hexagon. Is this hexagon equilateral? equiangular? What is its area?
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 Buying Paint and Shingles  Annie Fetter
Geometry, difficulty level 2. Figure out how many gallons of paint and how many bundles of shingles I need to buy to finish my new shed.
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 Calculating String Length  Annie Fetter
Geometry, difficulty level 2. Given the archery targets of two competitors, figure out which one has the shortest 'string length'.
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 Canadian Soccer  Judy Ann Brown
PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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 A Carpenter's Trisection  Annie Fetter
Geometry, difficulty level 3. Explain whether or not the given method of trisecting an angle, using only a carpenter's square, really works.
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 The Center of Gravity of a Quadrilateral  Annie Fetter
Geometry, difficulty level 3. Find the center of gravity of a quadrilateral.
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 Checking a Building Foundation for Square  Annie Fetter
Geometry, difficulty level 2. How can you determine whether a rectangle is square when all you have is string and a tape measure?
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 Chords and Arcs  Annie Fetter
Geometry, difficulty level 3. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The radius of the circle is 6 times the square root of 2. What is the length of the minor arc subtended by the chord?
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 Circle and Rhombus  Annie Fetter
Geometry, difficulty level 3. In the picture, we have a circle and a rhombus. BC is 6, AE is 4, angle DAE is 45 degrees, and AD is a diameter of the circle. How far is it around the perimeter of the whole figure?
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 Circle, Hexagon, & Triangle  Annie Fetter
Geometry, difficulty level 2. A regular hexagon and an equilateral triangle share three vertices and are inscribed in a circle with a radius of 8 units. What is the area of the region between the two polygons?
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 A Circle Inscribed in an Isosceles Triangle  Ilmar Vitsut
Geometry, difficulty level 4. Find the radius of a circle inscribed in an isosceles triangle with sides 12, 12, and 8.
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 Circle Intersections  Annie Fetter
Geometry, difficulty level 2. What is the maximum number of times that six circles of the same size could intersect?
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 Circles and Tangents  Annie Fetter
Geometry, difficulty level 3. AOD is a diameter of circle O. B is any point on the circle. At B, a tangent is drawn to the circle. From the center, O, a line is drawn parallel to AB, meeting the tangent at P. Prove that PD is tangent to
the circle.
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 Circumnavigating Circles  Annie Fetter
Geometry, difficulty level 3. The radii of two wheels are 10 vershoks and 5 vershoks and their centers are 30 vershoks apart. A belt goes around both of the wheels, crisscrossing between the two centers to form two internal tangents. What's the length
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 Congruence and Area  Annie Fetter
Geometry, difficulty level 3. "If two triangles have the same area, then they are congruent." Is this a true statement?
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 Congruent Chords and Circles  Annie Fetter
Geometry, difficulty level 4. Prove that two congruent chords in a circle are equal distances from the center of the circle.
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 Congruent Chords  Annie Fetter
Geometry, difficulty level 3. Two congruent circles are drawn, and four congruent chords are drawn, two in each circle, all perpendicular to the diameter through both circles. The distance between the two furthest chords is 20, and the distance between
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 Congruent Rectangles  Annie Fetter
Geometry, difficulty level 1. Seven congruent rectangles are arranged to form a larger rectangle. If the area of the large rectangle is 756 units^2, what's the perimeter of the large rectangle?
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 Construct an Isosceles Triangle  Annie Fetter
Geometry, difficulty level 2. Give at least three different ways to construct an isosceles triangle (a construction can be repeated over and over and in this case will always yield an isosceles triangle).
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 Constructing a Window  Annie Fetter
Geometry, difficulty level 4. Explain the shapes of the other four sides of a regular hexagonal window that's built between two wall studs 22.5" apart.
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 A Construction Puzzle  Annie Fetter
Geometry, difficulty level 3. Given angle PQR and point Y in the interior of the angle, construct XZ so that X lies on QP, Z lies on QR, and Y is the midpoint of XZ.
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 Coordinated Triangle?  Annie Fetter
Geometry, difficulty level 3. Triangle ABC has an area of 24 units^2. Point A is at (6,0); point B is at (10,0). Where can point C be? What if the triangle is
isosceles?
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 The Corner Banking of the Daytona Speedway  Annie Fetter
Geometry, difficulty level 2. Compare the corner banking at the Daytona Speedway, which is 31 degrees, with the roof on the house and garage that I helped build.
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 Counting Squares  Annie Fetter
Geometry, difficulty level 2. Count the total number of squares in the given diagram.
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 Descartes' Triangle?  Annie Fetter
Geometry, difficulty level 3. Two vertices of a triangle are located at (0,6) and (0,12). If the area of the triangle is 12 square units, where can the third vertex be? What if the triangle is also isosceles?
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 Diagonal Dilemma  Karen Cohen
Geometry, difficulty level 1. What is the area of the square ABCD that has a diagonal of length 12 cm?
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 The Diagonal Triangle  Annie Fetter
Geometry, difficulty level 1. A triangle is formed by connecting opposite vertices of a figure formed by two squares. Find the area of the triangle.
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 Different Views  Annie Fetter
Geometry, difficulty level 3. Given a front, top, and side view of an object, find the volume of that object.
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 Dilating a Quadrilateral  Annie Fetter
Geometry, difficulty level 3. Given two similar quadrilaterals on a coordinate grid, determine the ratio and center of dilation.
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 The Dimensions of a Hunting Platform  Annie Fetter
Geometry, difficulty level 2. I have a picture of a hunting platform, and I need help figuring out some of the dimensions.
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