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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Building a Geometric Proof [06/03/1999]

Can you explain how to do a two-column proof?

Explementary Angles [05/29/2003]

What do we call two angles that add up to 360 degrees?

Geometry Proofs [11/07/2001]

General and specific advice for a student having trouble writing proofs on her own.

Is a Sphere 2-D or 3-D? [8/8/1996]

Is a sphere a two- or a three-dimensional object?

Measuring Angles with a Protractor [02/28/2002]

I want to know how to measure acute, reflex and obtuse angles with a protractor.

Painting Cubes [01/06/2003]

How many unit cubes would be needed to create a cube with a side length of 3 units? If you painted the larger cube and broke it up into unit cubes, how many faces of each unit cube would be painted?

Remembering Area Formulas [12/23/2001]

Is there was a good way to help me memorize the formulas for areas of different shapes?

About Basic Geometry [10/14/1998]

Who developed basic geometry? What is it used for? Who uses it?

Abraham Kaestner and Euclid's Fifth (Parallel) Postulate [12/02/1996]

Where can I find information on Abraham Kaestner?

A-frame for Swing [07/26/1997]

I am trying to build a stand for a swing. The ends are A-frames out of 4 by 4's... what is the angle of the miter cut?

The Algebra of Complements and Supplements [01/25/1999]

What are complements and supplements? How do you translate these concepts into algebra?

Alternate and Corresponding Angles [10/21/1996]

Please explain corresponding and alternate angles.

Alternate Exterior Angles [06/03/2002]

What is an 'alternate exterior angle'?

Analytical Geometry [04/11/2002]

When two straight lines meet each other perpendicularly, the product of their slopes is -1. However, x and y axes meet at 90 degrees, but the product of their slopes is not -1. Why?

Angle Inscribed in a Semicircle [11/07/2001]

Prove that any angle inscribed in a semicircle is a right angle.

Angles as Turns [05/29/2003]

How can angles be negative?

Angles Greater than 360 Degrees [01/01/1999]

We know the definitions of acute, obtuse, and reflex angles, but we were debating what kind of angle a 425 degree angle is.

Angle, Side Length of a Triangle [9/4/1996]

What is the relation between the angles and side lengths of a triangle?

The Angles of a Roof [11/20/1995]

I am trying to build a model house but am having trouble with laying out the roof. The main part of the house has a peaked roof (an "A" frame house); the angle formed when the roof meets the ground is 60 degrees. There is an addition onto the A-frame with a 30 degree angle formed to the walls. What angle should the addition's roof be cut at so it meets the A-frame roof?

Angles of Stars [08/18/1997]

What are the interior and external angles of stars built on regular pentagons and octagons.

Angle Trisection: Construction vs. Drawing [10/17/2001]

Has anyone ever divided an angle into three equal parts by construction? I have been told it has not been accomplished.

Another Grazing Cow [6/7/1995]

A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing?

Ant and Rectangle [01/22/2001]

Does the ant walk along the diagonals of the rectangle?

Area and Perimeter: Isoperimetric Quotient [12/05/2001]

What is the isoperimetric quotient of a two-dimensional shape? Is it a measure of compression?

Area and Perimeter: Mowing the Lawn [6/1/1996]

How many circuits are necessary to cut half the lawn?

Area, Circumference of an Ellipse [7/29/1996]

How do I calculate the area and circumference of a given ellipse?

Are All Triangles Isosceles? [09/15/1999]

Can you help me find the flaw in this 'proof' claiming that all triangles are isosceles?

Are Angles Dimensionless? [08/31/2003]

If you look at the dimensions in the equation arc length = r*theta, it appears that angles must be dimensionless. But this can't be right. Or can it?

Area of a Circle with Radius less than 1 [02/18/2002]

If the radius is less than 1 it just gets smaller and you get a smaller area...

Area of an Ellipse Cut by a Chord [05/26/2000]

How can you calculate area of the part of an ellipse cut off by a chord, if you know the major and minor axes, and the chord?

Area of an Inscribed Quadrilateral [05/11/2000]

Given a quadrilateral where the midpoints of each side are connected to form a new quadrilaterals inside the first, what is the ratio of the area of the larger quadrilateral to the smaller one?

Area of a Rectangle Outside a Rectangle [6/11/1996]

Find the area of the concrete border of a rectangular swimming pool.

Area of a Reuleaux Triangle [06/13/2002]

Could you please help me find a formula to find the area of a Reuleaux triangle?

Area of Intersection of Two Circular Segments [04/20/2007]

Given a circle of radius r and center c, suppose two intersecting chords AB and CD (intersecting in P) form two circular segments. How do I compute the area of the intersection of the two circular segments?

Areas of House Lots [02/18/1998]

We have to determine sanitary sewer assessments of properties based on the square feet of their lots. Many lots are 4-sided but do not have any parallel lines...

Arrange 7 Points in a Plane... [10/05/1998]

Arrange 7 points in a plane so that if any three are chosen, at least 2 of them will be a unit distance apart.

Azimuth Angle [09/08/1998]

Can you give me the formula for the azimuth angle and explain some of the terminology?

Ball Bouncing off a Line Segment [05/04/2001]

If you take an arbitrary line on a 2D plane, e.g. x1y1 - x2y2, then take a point that moves about the plane, say pxpy, can you tell if this point has crossed the line at any time?

Barycentric Calculus [01/06/1999]

How does barycentric calculus compare with trilinear or cartesian calculus?

Betweenness of Points on a Line Idea and Proof [06/26/2008]

Could someone explain betweenness of points on a line and why it's important? I also don't understand the way my book proves it.

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