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Dr. Math FAQ:
Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
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Selected answers to common questions:
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
- 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
- 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
- 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
- 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
- Length of a Roll of Carpet [08/21/1997]
How can you determine the length of a roll of carpet without uncoiling
- 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
- 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.