Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #6
1. (Exercise 2C.3) Given ABC, draw line W V through A parallel to BC, line U W
through B paral
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #10
1. (Exercise 4A.2) Let U and V be points on sides AB and AC, respectively, of ABC
and suppose
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2012
Solutions to Assignment #5
Tinkering with triangles
In both of the questions below suppose D and E are the midpoints of s
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2012
Solution to Assignment #4
Similarity
Euclids Elements doesnt get into similarity until Book VI, but its a concept that
co
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2012
Solutions to Assignment #1
A geometry on a paraboloid
We will dene a geometry G of points and lines on (the surface of) t
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solutions to Problem Set #1
Please note that these solutions do not include any diagrams. To make sure you
understand how th
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #2
1. (Exercise 1B.7) Suppose BY and CZ are altitudes of ABC and |BY | = |CZ|. Show
that |AB| = |
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Take-Home Final Examination
Due on Friday, 22 December, 2006.
Instructions: Do all three of parts A C, and, if you wish, par
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solutions to Problem Set #3
1. (Exercise 1H.2) Show that the three medians of a triangle go through a common point
[the cent
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #1
1. Go through Euclids proof of Proposition I-1 in the Elements and identify at each step
the u
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solutions to Problem Set #2
1. (Exercise 1E.1) Draw two medians of a triangle. This subdivides the interior of the
triangle
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Problem Set #5
1. (Exercise 2A.3) Given acute angled ABC, extend the altitudes from A, B, and C
to meet the circumcircle at
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solutions to Problem Set #4
1. (Exercise 1H.6) In the gure below [Figure 1.45 in the text], line segments P A, P B,
and P C
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solution to Problem Set #6
1. Suppose ABC is not equilateral. Must the incentre of this triangle be on its Euler
line? Prove
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Fall 2006
Solutions to Problem Set #7
1. (Exercise 2E.2) Suppose that the centroid and incentre of ABC are the same point.
Prove that
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2012
Solutions to Assignment #6
Cevas Theorem
The following result appears to have been rst obtained by the Arab mathematician
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2013
Take-Home Final Examination
Due on Friday, 19 April, 2013.
Instructions: Do both of parts and , and, if you wish, part
as
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #9
1. (Exercise 3B.1) Line segments of length x and y have been drawn from vertex A of
ABC to bas
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Problem Set #11
Due on Friday, 4 April, 2008.
1. (Exercise 4B.2) Show using similar triangles that if Cevians AP , BQ, and
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #7
1. (Exercise 2E.3) Show that in a right triangle, the inradiius, circumradius, and
semiperimet
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #3
1. (Exercise 1E.3) Since a triangle is determined by angle-side-angle, there should be a
formu
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #5
1. (Exercise 2A.1) Show that quadrilateral ABCD can be inscribed in a circle if and
only if B
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Take-Home Final Examination
Due on Friday, 25 April, 2008.
Instructions: Do all three of parts A C, and, if you wish, part
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2011
Take-Home Final Examination
Due on Tuesday, 26 April, 2011.
Instructions: Do both of parts A and B, and, if you wish, par
v
Mathematics 226H Geometry I: Euclidean geometry
Trent University, Winter 2008
Solutions to Problem Set #4
1. (Exercise 1H.5) Given two points X and Y on a circle, a point P is chosen on line
XY , ou
Mathematics 2260H Geometry I: Euclidean geometry
Trent University, Winter 2012
Solution to Assignment #3
Angle-Angle-Side!
1. Show that the Angle-Angle-Side congruence criterion actually works. That i