 Splitting a Plane  Annie Fetter
Geometry, difficulty level 3. What's the greatest number of regions into which you can split a plane using six lines?
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 Splitting Space  Annie Fetter
Geometry, difficulty level 4. What's the greatest number of regions into which you can divide space using four planes?
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 Splitting up a Triangle  Annie Fetter
Geometry, difficulty level 4. Take any triangle ABC. Construct D and E as the midpoints of BC and
AB, respectively. Now construct DF and EF, where F is any point on AC.
How are the areas of the triangles related to the area of the
quadrilateral?
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 Square in a Right Triangle  Annie Fetter
Geometry, difficulty level 3. In the given picture, square DEFG is inscribed in a right triangle ABC (with right angle at B) with DG on AC, E on AB, and F on BC. If AD is 14 and GC is 29, what's the area of the square?
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 Squares on Squares  Annie Fetter
Geometry, difficulty level 3. Let P be the center of a 16" x 16" square as well as a vertex of
another 16" x 16" square that pivots freely around P. What is the
largest possible value for the area where these two squares overlap?
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 A Stellar Garden  Bill Marthinsen
PreAlgebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
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 Symmetry Surprise  Annie Fetter, Suzanne Alejandre
PreAlgebra, difficulty level 3. Identify the types of symmetries of each of three patterns.
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 A Tangent Square and Circle  Reza Kassai
Geometry, difficulty level 3. The square and circle below are tangent at one point and meet at four
other points, as shown in the picture. If the side of the square is 8
units long, what's the radius of the circle?
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 Teresa's Tiles  Kristina Lasher
Math Fundamentals, difficulty level 3. How many square tiles does Teresa need to cover her bathroom floor?
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 Tiling Triangles  Suzanne Alejandre
PreAlgebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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 Timber!  Steve Risberg
PreAlgebra, difficulty level 3. A tree breaks threeeighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree?
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 Transforming a Triangle  Annie Fetter
Geometry, difficulty level 1. Given two triangles on a coordinate plane, find a pair of transformations that will map the first triangle onto the second triangle.
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 Triangle in Motion?  Annie Fetter
Geometry, difficulty level 2. Given triangle ABC, the triangle is translated and then reflected, and
the locations of A' and A'' are given. Find the locations of B'' and C''.
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 Triangle Transformation  Annie Fetter
Geometry, difficulty level 3. Given triangles ABC and DEF on the coordinate plane and a list of transformations, explain how to map ABC onto DEF in only two steps.
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 TV Dimensions  Annie Fetter
Geometry, difficulty level 2. If the aspect ratio of a TV is 16:9 and the diagonal measures 50
inches, what are the dimensions of the screen?
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 Two Times Two Angles  Annie Fetter
Geometry, difficulty level 3. The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle.
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 Up Periscope!  Annie Fetter
Geometry, difficulty level 2. Given a diagram of a broken submarine periscope, explain which angles need to be equal in order to for the image to reach the eyepiece.
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 Waiting for Hot Water  Annie Fetter
Geometry, difficulty level 2. If a water pipe is 1/2" in diameter, the faucet is about 35 feet from the hot water tank, and the faucet runs at 3 gallons per minute, how long will it take the hot water in the tank to reach the faucet?
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 The Water in My Pool  Leigh Nataro
Geometry, difficulty level 2. Based on one measurement taken from the edge of my circular pool,
what is the volume of my pool?
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 What's My Angle?  Annie Fetter
Geometry, difficulty level 2. Given line AE, point C between A and E, ray CB perpendicular to line AE, and point D on the same side of AE as point B. If CD equals DE and angle CDE is x degrees, what is the angle measure of angle BCD?
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 What's This Polygon?  Annie Fetter
Geometry, difficulty level 4. Triangle PQR is inscribed in a circle. If PR is a side of a 21sided inscribed regular polygon, PQ is a side of a 28sided incribed regular polygon, and QR is a side of an nsided inscribed regular polyon, find a possible
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 Where's J?  Annie Fetter
Geometry, difficulty level 2. Given an isosceles triangle with one base vertex (O) on the origin, the other base vertex (J) on the positive xaxis, and the top vertex at the point (e,f), find the coordinates of J.
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 Who Wants to be an Archery Champion?  Annie Fetter
Geometry, difficulty level 2. To determine the winner, calculate the "string length" for each of two archery rounds.
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 Winning at Biathlon  Annie Fetter
Geometry, difficulty level 3. Figure out which of two fictional biathletes will win a race.
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 Wraparound Universe  Jeff Weeks
PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
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