Math Forum - Problems Library - All Geometry Problems

_____________________________________
diamond Library of Math Forum Problems

Primary Math Fundamentals Pre-Algebra
Algebra Geometry Discrete Math Trig/Calculus
_____________________________________
(membership required) || Become a Member || Learn about Membership
_____________________________________

TOPICS
space

This page:
  all geometry checkmark

About Levels
of Difficulty

Geometry
  lines/angles
  triangles
  quadrilaterals
  polygons
  circles
  perimeter, area,
    volume
  similar/congruent
  right triangles
  transform/symmetry
  construction/locus
  coordinate geometry
  modeling/applications

Browse all
Geometry
Problems

Geometry
Home

About the
PoW Library

Browse all Geometry Problems of the Week

Participation in the Geometry Problems of the Week allows teachers and students to address the NCTM Problem Solving Standard for Grades 9-12, enabling students to build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; and monitor and reflect on the process of mathematical problem solving.

For background information elsewhere on our site, explore the High School Geometry area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Geometry in our Internet Mathematics Library.


Access to these problems requires a Membership.

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? ... more>>

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? ... more>>

Analyzing Angles - Annie Fetter
Geometry, difficulty level 2. Given some information about angles in a picture, figure out some of the angle measures. ... more>>

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? ... more>>

Ants Marching - Annie Fetter
Geometry, difficulty level 2. Traveling along the edges of a cross section of the cube, find the length of the shortest possible path from one corner of a cube to the opposite corner, as well as the longest possible path between the same corners. ... more>>

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? ... more>>

Approximating Pi - Annie Fetter
Geometry, difficulty level 3. Approximate the value of pi using polygons instead of a circle. ... more>>

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. ... more>>

Arda and Brooke's Catapult - Annie Fetter
Geometry, difficulty level 2. Does Arda's method for measuring the distance across the river really work? ... more>>

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? ... more>>

Area of a Rhombus - Annie Fetter
Geometry, difficulty level 2. Find the area of a rhombus, given one angle measure and the length of the longer diagonal. ... more>>

Arranging Rectangles - Annie Fetter
Geometry, difficulty level 3. Help Kasim decide if his arrangement of rectangles could ever form a square. ... more>>

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? ... more>>

Assessing Seismic Risk - Craig Foster and Annie Fetter
Geometry, difficulty level 3. Figure out how likely it would be for an earthquake to occur within certain distances of a building. ... more>>

Beach Boys - Steve Risberg
Geometry, difficulty level 3. Help Skip and Gil find the height of the cruise ship. ... more>>

Beyond Exterior Angles - Annie Fetter
Geometry, difficulty level 2. Extend two sides of the given polygon and determine the angle at which the new lines meet. ... more>>

Bouncing Billiards - Annie Fetter
Geometry, difficulty level 1. Help Maria decide the angle that will sink her cue shot after four bounces. ... more>>

Boxing Up Harry's Broom - Annie Fetter
Geometry, difficulty level 1. Help Harry find the right size box for his broom. ... more>>

Broken Pottery - Annie Fetter
Geometry, difficulty level 2. Explain how to find the center of this sherd. ... more>>

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. ... more>>

Building a Regular Hexagon - Annie Fetter and Steve Weimar
Geometry, difficulty level 3. How do you form a regular hexagon by attaching rectangles to the sides of an equilateral triangle? ... more>>

Building a Vaulted Ceiling - Annie Fetter
Geometry, difficulty level 4. An eyebrow window is a 15-inch-deep slice off an 8.5-foot circle. How wide will the base of the window be? ... more>>

Building Bookshelves - Steve Weimar
Geometry, difficulty level 2. Merriem and Emmanuel's new bookshelf hits the ceiling when they try to put it in place. Explain why, and help them figure out how much to cut off the bottom so that it will fit. ... more>>

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? ... more>>

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. ... more>>

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'. ... more>>

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. ... more>>

Circle Derby - Terry Trotter
Geometry, difficulty level 2. Determine which dot has the small angle to go and which has the shortest distance to go in this race around a circle. ... more>>

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. ... more>>

Circle Intersections - Annie Fetter
Geometry, difficulty level 2. What is the maximum number of times that six circles of the same size could intersect? ... more>>

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. ... more>>

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, criss-crossing between the two centers to form two internal tangents. What's the length of the belt? ... more>>

Clever Cuts - Annie Fetter
Geometry, difficulty level 2. Find three different ways to cut a hexagonal cake into six congruent pieces. ... more>>

Comparing the Areas of Two Squares - Annie Fetter
Geometry, difficulty level 3. Given two squares, one with the diameter of a circle as an edge, the other inscribed in the circle. How do the areas of the squares compare? ... more>>

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? ... more>>

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. ... more>>

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 two chords of the same circle is 8. What's the area of one of the circles? ... more>>

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? ... more>>

Congruent Rectangles Help - Annie Fetter
Geometry, difficulty level 2. Find some possible areas for the large rectangle shown in the given picture. ... more>>

Constructing a Tangent - Annie Fetter
Geometry, difficulty level 3. Explain why this construction of a tangent works. ... more>>

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. ... more>>

Constructing the Great Pyramid - Annie Fetter & Suzanne Alejandre
Geometry, difficulty level 2. Figure out if the instructions provided will result in a scale model of the Great Pyramid of Giza. ... more>>

The Coordinated Quadrilateral - Annie Fetter
Geometry, difficulty level 3. A quadrilateral has vertices at (-3,6), (-1,-2), (7,-4), and (5,4). What kind of quadrilateral is it? ... more>>

Page:  1  2  3  4  5  6 [next>]


[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2012 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.