Geometry Foundations
Name the three undefined terms of geometry.
Point, line, and plane.
State the Pythagorean Theorem.
In a right triangle, a^{2} + b^{2} = c^{2} (where c c c is the hypotenuse).
Name the similarity criterion that uses two pairs of congruent angles.
AA Similarity.
State the formula for the volume of a cylinder.
V = \pi r^{2} h
State the Commutative Property of Addition.
a + b = b + a
What does the word “geometry” literally mean?
“Earth measurement” (from the Greek geo = earth + metron = measure).
State Euclid’s postulate about two points.
Two distinct points determine a unique line.
State the Triangle Inequality Theorem.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Name the similarity criterion that uses three pairs of proportional sides.
SSS Similarity.
State the formula for the volume of a cone or a pyramid.
V = \frac{1}{3} Bh (where B is the area of the base).
State the Commutative Property of Multiplication.
a \times b = b \times a
What did the ancient mathematician Pythagoras supposedly make his students swear an oath about?
Never to eat beans (and also to keep the discovery of irrational numbers secret).
How many planes are determined by three non-collinear points?
Exactly one plane.
What construction divides an angle into two congruent angles?
An angle bisector.
Name the similarity criterion that uses two proportional sides and the included angle.
SAS Similarity.
State the formula for the surface area of a sphere.
SA = 4\pi r^{2}
State the Associative Property of Addition.
(a + b) + c = a + (b + c)
True or False: The ancient Greeks (including Euclid) already knew about the number zero.
False. The Greeks did not have a symbol or concept for zero as a number. Zero came later from Indian mathematicians.
What two tools are used in classical geometric constructions?
Compass and straightedge (unmarked ruler).
In a right triangle with legs 3 and 4, what is the hypotenuse? (Quick check of the theorem)
5 Because
( 3^{2} + 4^{2} = 5^{2} ).
If the side ratio of two similar figures is k k k, what is the ratio of their areas?
k^{2} (areas scale by the square of the side ratio).
State the formula for the space (body) diagonal of a rectangular solid.
d = \sqrt{l^{2} + w^{2} + h^{2}}
State the Associative Property of Multiplication.
(a \times b) \times c = a \times (b \times c)
John Saxon (the guy who wrote your textbook) had an unusual first career. What was it?
He was a U.S. Air Force officer and engineer before he became a math teacher and textbook author.
What construction creates a line that is perpendicular to a segment at its midpoint?
The perpendicular bisector.
Why can sides of lengths 3, 5, and 9 not form a triangle?
They violate the Triangle Inequality (3 + 5 = 8 < 9 ).
In similar figures, corresponding sides are ________ and corresponding angles are ________.
proportional; congruent.
A sphere has volume 288\pi. . What is its radius?
6 (because \frac{4}{3}\pi r^{3} = 288\pi \Rightarrow r^{3} = 216 \Rightarrow r = 6 ).
State the Distributive Property.
a(b + c) = ab + ac
What is the only number that has the same number of letters as its value in English?
Four (F-O-U-R has 4 letters).