See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Two-Dimensional Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Pythagorean theorem proofs.
- No Slope: An Ambiguous Term [05/08/2003]
What is the distinction between a line with a slope of zero and a
line with no slope?
- No Thickness [12/08/2002]
What is a location in space that has no thickness?
- Obtuse and Oblique [7/29/1996]
Are the terms "obtuse" and "oblique" interchangeable?
- One Dimension [05/13/2003]
Is there such a thing as 1D?
- The Order of a Proof [01/29/1999]
How can you figure out what order to put your proof in?
- Parallel Curves [05/21/1997]
If line segments can be parallel, can curves be parallel? Are lines of
- Parallel Lines [12/31/1998]
What are some ways of proving lines parallel - geometrically and
- Parallel Lines and Three-Dimensional Space [12/18/2005]
My math book says two lines that are each perpendicular to the same
third line are not necessarily parallel to each other. How can that
be? They would not touch, and isn't that the definition of parallel
- Parallel Lines and Transversals Proof [09/28/1998]
Prove: If two angles are cut by a transversal and the same-side angles
are supplementary, then the lines are parallel.
- Perimeter of a Line [08/25/2002]
Does a line have perimeter?
- Perimeter of Two Similar Objects [2/16/1996]
Why do you lose area in a 4 x 12 rectangle as compared to an 8 x 8
square? Each has the same perimeter.
- Planting Trees [08/13/2002]
I have to plant 10 trees in 5 rows with 4 trees in each row.
- Point and Line [04/07/2001]
How does something without dimension create something with dimension?
- Polygon Angles [02/14/1997]
What is the sum of the measure of the angles in polygons with sides 3-50?
- Polyominoes [09/08/1997]
I am using polyominos, but I do not know how to tell my dad what they
are. How can I tell him so he will know?
- Polyominos [08/11/1999]
What is the definition of a polyomino?
- Precision in Measurement: Perfect Protractor? [10/16/2001]
Given that protractors are expected to be accurate to the degree, and in
some instances the minute or second, how are angles accurately
constructed and marked?
- Proofs and Reasons [01/03/1999]
Write a two-column proof for the following theorem: AC is greater than BC
and AP = BQ.
- Proportions of Exact Enlargements [03/18/1998]
How are two objects related if one is an "exact enlargement of the
- Ray, Line Segment, Line [08/23/1997]
I need to know definitions for ray, line segment, and line.
- Rays and Angles [11/24/1997]
Do rays have an arrow on both ends, or is that an angle?
- Reading a Protractor [9/8/1996]
Which side of a protractor scale do you use?
- Reflex Angle [11/30/1998]
What is a reflex angle?
- The Relation of Perimeter to Area [10/2/1995]
I'm puzzled by the ability of two fences with the same perimeter to have
very different areas inside them. I realize by LxW an 8' x 10' fence will
have more area than a 6' x 12' fence, but WHY? Both fences have 18'
surrounding them but different areas. Also does a circle or a square
conserve more area with identical perimeters?
- Short History of Geometry [09/15/2001]
Were there any people who helped to develop geometry besides Euclid?
- Six Lines Make Twelve Triangles [11/06/2002]
How can I use 6 lines to make 12 triangles?
- Square Feet [4/13/1996]
I need to know how to compute square feet for some cabinets that I have
to move in a room.
- Straight Angle vs. Line [09/07/1997]
Why is a straight angle (line) not considered an angle?
- Subtend [07/23/1997]
Please give me the definition of the word "Subtends."
- Surface Area and Volume: Cubes and Prisms [05/27/1998]
What is the definition of surface area and volume? What are the
differences and similarities between surface area and volume?
- Surface Area Block Problem [08/05/1997]
How much foil is needed to wrap all the slabs of cheese cut from the
- Thinking About Proofs [09/24/1997]
How do you know what statement to write next in a proof? What reasons do
- Thinking about the Maximum Area Enclosed by a Fence [04/15/2004]
You have 2000 meters of fencing. What is the largest area you can
enclose with it using various shapes?
- Three Cuts and Seven Pieces [01/18/1999]
Is there any way that you can cut a pie into seven pieces with just three
- Three-dimensional Counterparts for Two-dimensional Objects [03/04/1998]
Three-dimensional counterparts for lines, polygons, perpendicular lines,
and collinear lines.
- A Three-Legged Stool [06/26/2001]
Why is a three-legged stool steady, while a four-legged stool can be
- Tiling a Floor [06/30/1999]
How many square yards is a 12ft. by 15ft. room? How many 8" x 8" tiles
would you need for a 30 sq. ft. room?
- Traceable Mathematical Curves [10/27/1997]
Is there any way to tell just by looking if a curve is traceable or not?
Is there some property of a curve that will tell you this? Do curves have
- Translation [9/11/1996]
What does translation mean?
- Translation, Reflection, Rotation [05/16/2001]
What is the difference between slide, flip, and turn?