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Dr. Math FAQ:
Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
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Selected answers to common questions:
Pythagorean theorem proofs.
- 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.
- 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
- 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?
- Number of Equations Needed in a Simultaneous Linear System [10/29/2003]
Could you tell me why we need the same number of equations as
variables in order to get a unique solution to a system of
simultaneous linear equations?
- Obtuse and Oblique [7/29/1996]
Are the terms "obtuse" and "oblique" interchangeable?
- Optimization: Minimum Area [11/07/1997]
How do you fold a piece of paper (rect. with width a and unlimited
length) so one corner just reaches the righthand side for minimum area?
- The Order of a Proof [01/29/1999]
How can you figure out what order to put your proof in?
- 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.
- Parallel Lines, Concentric Circles [04/24/2003]
If parallel means that two lines never intersect, would the lines
that form a circle drawn inside another circle be considered parallel?
- Parallel Lines: Euclidean and Non-Euclidean Geometry [4/25/1996]
If two lines are parallel, can they intersect?
- Parallel Lines in Projective Space [05/18/1998]
Do parallel lines intersect at infinity? Is this in projective space?
- Parallel Lines: Two Column Proof [09/09/1998]
Could you break down the steps in doing a two column proof to show that
two lines are parallel given certain congruent angles?
- Path Length or Displacement? [10/17/2001]
A body moves from A due east 5m to B, then from B due north 6m to C, and
from C due west 5m to D. Calculate total distance covered from A to D.
- Path Less Than 1 + sqrt(3) [03/18/2003]
Is there a way to connect the four vertices of a square (of side
length 1) such that the path travelled is less than 1 + sqrt(3)?
- Perimeter of 1000m [07/13/1999]
Find the shape with a perimeter of 1000m and the largest possible area.
- Perimeter of a Line [08/25/2002]
Does a line have perimeter?
- Perimeter of a Reuleaux Triangle [04/15/2001]
How can I find the perimeter of a Reuleaux triangle of width h?
- Planes and Lines [10/26/1996]
Do planes and lines contain the same number of points?
- 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?
- Point Equidistant from 3 Other Points [04/11/1999]
How do you find a point that is equidistant from three other points?
- 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?
- 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?
- Problems about the Angle between the Hands of a Clock [09/08/2005]
At 1:45, the angle between the hands of a clock is 142.5 degrees. When
is the next time the angle between the hands will be 142.5 degrees? In
addition to that specific problem, this talks about general strategies
for solving problems involving angles between the hands of a clock.
- Proof of Congruency [10/13/1996]
Line PR bisects angles QPS and QRS; prove that segments RQ and RS are
- Proof of Heron's Area Formula [12/30/1997]
I need to write a proof of Heron's Area Formula.
- Proof of Perpendicularity [10/23/1999]
How can you prove that two lines (neither vertical) are perpendicular if
and only if the product of the gradients is equal to -1?
- 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
- Proving Lines Congruent [03/29/2002]
Prove line AL is congruent to line CM.
- Ratios, Geometry, Trigonometry [06/10/1999]
A homeschool teacher asks for help with triangles, flagpoles, and
- Real-World Carpentry and Trigonometry [11/19/2002]
I'm trying to come up with a formula to calculate the height of an arc
at the midpoint of the chord that defines it knowing only the length
of the arc and the length of the chord.
- Reflection Points on a Circle-Shaped Mirror [09/30/2003]
Points A and B are located within a circle. If A were a light emitting
point and B a light receiving point, then B would receive light from
points P on the circle. How can I find these points?
- Reflection, Rotation, Translation and Glide Reflection [06/27/2005]
Considering the four symmetry transformations--reflection, rotation,
translation, and glide reflection--is it possible to express
transformations in the two-dimensional plane as a composition of at
most three reflections?
- Reflex Angle [11/30/1998]
What is a reflex angle?