Ask Dr. Math

High School Archive

Browse High School Euclidean/Plane 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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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?

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 algebraically?

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 lines?

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 congruent.

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 other"?

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 circles.

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?

Research in dynamic geometry [08/27/1997]

I would like to know about research into learning Geometry using Dynamic Geometry environments.

Reuleaux Curve Applications [05/25/2002]

What is the Reuleaux curve used for?

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