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Dr. Math FAQ:
Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Pythagorean theorem proofs.
- 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
- 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
- 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
- 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 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 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
- 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
- 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
- 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
- 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.