Ask Dr. Math

Middle School Archive

Browse Middle School Two-Dimensional Geometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Classifying quadrilaterals.
    Pythagorean theorem proofs.

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Euler's Formula [11/26/2001]

I have to find Euler's formula for two-dimensional figures and explain it at a university level and at an elementary-school level.

Figuring Out Formulas for Area [08/24/1999]

How can I remember formulas for squares, triangles, cylinders, etc?

Figuring Square Footage and Yardage [12/14/2002]

What is the exact calculation used in order to determine square footage or yardage of a given room?

Finding Areas of Different Polygons [09/02/1997]

Could you please tell me how to work out the area for an equilateral heptagon, octagon, nonagon, decagon, unedecagon, and dodecagon?

Finding Captain Kidd's Treasure [05/17/2000]

How can you find Captain Kidd's treasure if you can't find the tree referenced in the instructions?

Finding Line Segment Lengths [12/21/2001]

Can you help me find line segments AB and BC if points A,B,C, and D are collinear with B between A and C and C between B and D...?

Fitting a Picture to a Frame [11/14/1996]

I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

Flatland, by Edwin Abbott [8/21/1996]

I need any info about the book FLATLAND by Edwin Abbott and how it can be used in the classroom.

Flips, Reflections, Rotation, and Quadrants [11/10/1998]

These terms are being used to describe the movement of shapes. What do they really stand for?

Geometric Probability [05/23/2001]

If an arrow is equally likely to hit anywhere inside a circular target that is 3 feet in diameter, what is the probability that it will hit inside a bull's-eye that is 6 inches in diameter?

Geometric Proofs [11/28/1998]

I am tring to help a friend learn geometric proofs. Do you have any suggestions?

Geometry Books [4/17/1996]

I am having trouble finding an instructive book on geometry. Do you have any suggestions?

Geometry Project [11/1/1994]

Think of three examples of geometry in the real world, one non-man-made (found in nature).

Geometry Proofs: Lines and Planes [11/08/1998]

Show that two intersecting lines intersect in exactly one point...

Geometry Proofs with Lines [2/6/1996]

Prove that if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Grad as a Measure of an Angle [03/20/2002]

I would like to know about the origins, use in the past, and whether (and how) the grad is used now.

How Can a Line Have Length? [04/14/1998]

If a Euclidean point has no length, how can a union of Euclidean points form a Euclidean line segment with length?

If You Know Perimeter, Can You Find Area? [6/30/1996]

Can one determine the acreage of an irregularly shaped field if only the distance around the edge of the field (in feet) is known?

Instruments for Measuring Angles [09/28/2001]

I need the name, picture, or description of five devices used to measure angles.

Intersection of Circles [10/08/1998]

I do not understand the term intersection in geometry.

Intersection of two angles [8/31/1996]

Draw a diagram in which the intersection of angle AEF and angle DPC is ray ED.

Introduction to Quadrants in the Coordinate Plane [02/05/2004]

What is a quadrant? How do you find it? I had to identify 9 ordered pairs on a graph. Now I need to also name the quadrant each one is in.

Is a Star Concave or Convex? [4/2/1996]

Is a star-shaped polygon convex?

Is Henry Guilty? (Geometry Puzzle) [6/10/1996]

In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road...

Jobs That Use Geometry [12/18/2001]

I would like to learn how geometry is used in real life. What jobs involve geometry?

Join the Dots [09/02/2001]

Given 9 dots in a square, how can you connect them with only 4 lines without picking up your pencil or going through a dot more than once?

Left Angles [06/01/1999]

What is a left angle?

Linear and Board Feet [01/04/1999]

Can you explain the terms linear foot and board foot as they are used in the lumber industry?

Linear Footage [04/20/2002]

There is a fence I want to buy, but the ad says '4 foot tall, 50 linear feet. What is a linear foot compared to a regular foot?

Math in soccer [05/21/1999]

How is math involved in soccer?

Maximum Number of Intersections of n Distinct Lines [10/07/1998]

Find a pattern for the maximum number of intersections of n lines, where n is greater than or equal to 2.

The Meaning of Locus [03/04/2003]

What is the locus of points equidistant from two parallel lines 8 meters apart?

Measuring Angles Without a Protractor [01/26/1999]

Given an isosceles trapezoid and one angle, how would we find the other three angles?

Mobius Strips, Spheres, and Dimensionality [05/28/2003]

Is a Mobius Strip 2-D or 3-D? Or is it 1-D? What about a sphere?

Names of Triangles and Angles [07/25/2001]

My teacher told me to find names of triangles other than equilateral and isosceles.

Net of a Box [05/23/1999]

Choose dimensions (length, width, and height) and find the surface area and volume of a box; then draw a flat pattern of the box.

Net of a Hexagonal Pyramid [02/05/2001]

How would you draw the nets of a hexagonal pyramid and a rectangular prism?

Nets in a Geometrical Sense [03/07/1999]

What is the "net" of a shape?

Non-Euclidean Geometry for 9th Graders [12/23/1994]

I would to know if there is non-euclidean geometry that would be appropriate in difficulty for ninth graders to study.

Non-parallel Glide Reflections [10/21/1998]

A glide reflection consists of a line reflection and a translation parallel to the reflection. What if the translation is not parallel to the reflection?

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