Selected solutions for Math 445 HW7, Summer 2013
John H. Palmieri
August 20, 2013
Theorem (Theorem 12.8, Median Concurrence Theorem, Exercise 12I). The medians of a triangle are
concurrent, and the distance from the point of intersection to each vertex is
Selected solutions for Math 445 HW1, Summer 2013
John H. Palmieri
August 6, 2013
Theorem (Diagonal Criterion for Convexity, Theorem 9.4, Exercise 9B).
lateral intersect, then the quadrilateral is convex.
(a) If the diagonals of a quadri-
(b) If a quadrila
Selected solutions for Math 445 HW2, Summer 2013
John H. Palmieri
August 6, 2013
Theorem (Theorem 9.19, Exercise 9D). Suppose ABCD is a quadrilateral.
(a) If its diagonals bisect each other, then ABCD is a parallelogram.
(b) If its diagonals are congruent
Math 445
Wednesday, August 12
Summer 2015
Quiz 3
Name:
Prove the following statement in Euclidean geometry, using everything in your book up to and including
Chapter 14.
Theorem In a triangle ABC the centroid, incenter, circumcenter and orthocenter are th
Math 445
Wednesday, August 05
Summer 2015
Quiz 2
Name:
The statements below refer to the following diagram. All you know about this diagram is that 4ABC is a
triangle and D and E are points such that A E C and A D B. The angles 1, 2, 3 and 4 are defined
a
Math 445
Friday, July 31
Summer 2015
Quiz 1
Name:
For each of the following classes of quadrilaterals in Euclidean geometry I will list some properties. Next
to each property mark one of the following letters:
A if all quadrilaterals of that type have th
Name
Student Number
Practice Final
Math 445A: Geometry for teachers
June 1, 2014
Problem Total Points
1
2
3
4
5
6
7
8
Total
Score
- You may use the lists of postulates and theorems distributed in class and two-sided page of
your own notes prepared for the
Name
Student Number
Practice MIDTERM
Math 445A: Geometry for teachers
April 25, 2014
Problem Total Points
1
10
2
10
3
10
4
10
5
10
6
10
Total
60
Score
- You may use the distributed lists of axioms and theorems and one-sided page of your own
notes prepared
Name
Student Number
MIDTERM
Math 445A: Geometry for teachers
May 2, 2014
Problem Total Points
1
10
2
10
3
10
4
10
Total
40
Score
- You may use the lists of axioms and theorems and one-sided page of your own notes prepared
for the midterm.
- No other notes
Selected solutions for Math 445 HW10, Summer 2013
John H. Palmieri
August 20, 2013
Theorem (Theorem 17.5, Properties of Saccheri quadrilaterals, Exercise 17B). Every Saccheri quadrilateral
has the following properties:
(a) It is a convex quadrilateral.
(b
Selected solutions for Math 445 HW7, Summer 2013
John H. Palmieri
August 20, 2013
Theorem (Exercise 17C-D). Procluss postulate is equivalent to the EPP, and the transitivity postulate is
equivalent to the EPP.
Proof. For Procluss postulate, we know that i
Selected solutions for Math 445 HW6, Summer 2013
John H. Palmieri
August 20, 2013
Theorem (half of Theorem 14.4, Exercise 14A). Suppose C is a circle and is a secant line that intersects
C at A and B . Then every point of that is not in AB is in the exter
Selected solutions for Math 445 HW5, Summer 2013
John H. Palmieri
August 20, 2013
Garelds proof of the Pythagorean theorem, Exercise 13A. Here is the picture:
E
B
c
a
b
C
A
D
We start with a right triangle ABC with right angle C , leg lengths a and b (for
Selected solutions for Math 445 HW4, Summer 2013
John H. Palmieri
August 6, 2013
Theorem (Theorem 12.5, SSS Similarity Theorem, Exercise 12A). If
that AB/DE = AC/DF = BC/EF , then ABC DEF .
ABC and
DEF are triangles such
Proof. Let D E be a segment congru
Selected solutions for Math 445 HW3, Summer 2013
John H. Palmieri
August 6, 2013
Theorem (Theorem 11.10, Area of a Triangle, Exercise 11A). The area of a triangle is equal to one-half
the length of any base multiplied by the corresponding height.
Proof. F
Math 445
Monday, August 17
Summer 2015
Quiz 4
Name:
The statements below refer to the following diagram. All you know about it is that ABCD is a convex
quadrilateral.
For each of the statements below circle
Euclidean if the statement is always true in Eu