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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.

How to Build a Proof [05/18/1999]
Given: Triangle ABC is a right triangle... Prove: Angle A and angle B are complementary angles.

How to Motivate Students to Learn Math? [03/06/2008]
Dr. Ian replies to a question about motivating students to learn about special quadrilaterals with some excellent general advice on motivation, math education, and real life application of mathematics.

If You Know Perimeter, Can You Find Area? [6/30/1996]
Can one determine the acreage of an irregularly shaped field if only the distance around the edge of the field (in feet) is known?

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.

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