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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Indirect Proof of Parallel Lines [11/26/2001]

I have asked my high school geometry class to prove indirectly that parallel lines have the same slope. Unfortunately, I cannot figure out how to do it myself...

Inscribed Angle Theorem [01/21/1999]

Can you help me prove that an angle inscribed on the same arc as a central angle is equal to one half that central angle?

Instruments for Measuring Angles [09/28/2001]

I need the name, picture, or description of five devices used to measure angles.

Intercept of a Line with a Circle [05/28/1999]

What is the general equation for the intercept between a circle x^2 + y^2 - 2fx - 2gy + d = 0 and a line ax + by + c = 0?

Intersecting Angles [08/26/1998]

Draw a diagram in which the intersection of angle AEF and angle DPC is ray ED.

Intersecting Chords [06/09/2002]

Two chords of a circle, AB and CD, intersect at point E. Prove that AE*EB = CE*ED.

Intersecting Vectors and the Dot Product [04/24/1998]

Each of the following geometrical theorems can be proved with vectors, using the dot product...

Introduction to Quadrants in the Coordinate Plane [02/05/2004]

What is a quadrant? How do you find it? I had to identify 9 ordered pairs on a graph. Now I need to also name the quadrant each one is in.

Is Geometry a Language? [01/28/2002]

I have to write an essay to defend or criticize the statement, "Geometry is a Language."

Is Henry Guilty? (Geometry Puzzle) [6/10/1996]

In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road...

Isoperimetric Inequalities [12/16/1995]

How can I prove that a circle has more area inside given its border length than any other shape?

Isoperimetric Quotient [03/11/2002]

Is there an equation for the ratio of surface area to volume?

Isosceles Trapezoid Proof [01/18/2002]

Given: ABCD is an isosceles trapezoid with bases BC and AD. Prove: ABCD is an isosceles trapzoid.

Jobs That Use Geometry [12/18/2001]

I would like to learn how geometry is used in real life. What jobs involve geometry?

Ladder Puzzles [03/16/2001]

Two ladders are leaning opposite ways between two buildings... at what height above the ground do they cross? How wide is the alley?

Land Plot Area [08/28/2002]

I have a parcel of land. The surveyor has determined it to be 624,630.88 square ft. and 14.340 acres. The legal description is 15.8 acres. How can I figure out the square footage?

Length of a Copper Helix [11/15/1998]

Can you help me find a formula to determine the length of straight wire needed to form a helix of a certain length when twisted with another wire?

Length of a Roll of Carpet [08/21/1997]

How can you determine the length of a roll of carpet without uncoiling it?

Light Beam Reflection [01/31/2002]

Four mirrors form a rectangle 3 m by 2 m. A light beam is shone from A at 45 degrees. Which corner does the beam strike first?

Linear and Board Feet [01/04/1999]

Can you explain the terms linear foot and board foot as they are used in the lumber industry?

Linear Footage [04/20/2002]

There is a fence I want to buy, but the ad says '4 foot tall, 50 linear feet. What is a linear foot compared to a regular foot?

Line or Ray Longer? [12/11/2001]

Which is longer, a ray or a line?

Line with Small Compass and Straightedge [10/16/1996]

Construct a line segment joining two points farther apart than either a compass or the straightedge can span.

Locating a Ship Using Three Angles [07/07/1999]

A ship's navigator saw landmarks in the distance at points A, B, and C, found angles ASB, BSC and CSA, then located the three points on a map to find the exact position of her ship. How did she do it?

Locus [05/03/1999]

What is a locus?

Mars '98 Lander [06/18/1997]

Given an arbitrary quadralateral in which all interior angles and two opposite sides are known, how do you find the other sides?

Math in soccer [05/21/1999]

How is math involved in soccer?

Maximization problem [11/29/1994]

A window is to have the shape of a rectangle topped by a semi-circle. Suppose that the semi-circle part of the window admits one-half as much light per square foot as does the rectangular part. What are the dimensions x and y of the window admitting the most light?

Maximizing Window Area [02/24/1997]

Maximize the area of a Norman window (rectangular with a semicircle on top) while minimizing the length of the perimeter.

Maximum Angle between Perpendicular Bisectors [06/11/1999]

Which four points on the circumferences of two non-intersecting circles will yield the maximum angle between the two perpendicular bisectors produced by their joins?

Maximum Fenced Area, One Side a Barn [10/16/2001]

Solve: y = 70x - 2x^2: find the maximum fenced area if one side is a barn. Why is the rectangle made up of two equal squares?

Maximum Number of Intersections of n Distinct Lines [10/07/1998]

Find a pattern for the maximum number of intersections of n lines, where n is greater than or equal to 2.

The Meaning of Locus [03/04/2003]

What is the locus of points equidistant from two parallel lines 8 meters apart?

Meaning of '-ominoe' [11/07/2001]

We are drawing pictures of dominoes, triominoes, tetrominoes, and pentominoes. What is the meaning of the root "ominoe"?

Midpoint Formula and Trisection Points [09/05/2003]

Show that ((1/3)(2x_1+ x_2), (1/3)(2y_1+y_2)) is one of the points of trisection of the line segment joining (x_1,y_1) and (x_2,y_2).

Minimum Distance from a Point to a Line [7/10/1995]

Find all the values of b such that the minimum distance from the point (2,0) to the line y = 4/3x+b is 5.

Miter Angle of a Pipe [02/10/1999]

Find the miter angle of a pipe of certain shape.

More on Geometry Proofs [12/11/2001]

I don't understand how to get from the given to the prove part. All the statements sound the same.

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?

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