University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 5 - Solutions
1. The quadrilateral BV P U is cyclic (BV P = , so V is on the circle of diameter BP ;
2
also, since BUP = , U is on
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 1 - Solutions
A*.
1
c2 = (b a)2 + 4 ab
2
2
2
2
c = b 2ab + a + 2ab
c2 = b2 + a2
B*. See Figure 1. As the hint says, construct the
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 2 - Solutions
1.* See Figure 1. We need to show that AB = BC . To this end, we calculate the angle
CAB . In the triangle ABC , the
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 4 - Solutions
1.* (a) Since IB is on the internal bisector through B we have
dist(IB , AB ) = dist(IB , BC ).
Since IB is on the e
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 6 - Solutions
1. We start with the left-hand side and write it as follows:
4b2 c2 (b2 + c2 a2 )2
= (2bc)2 (b2 + c2 a2 )2
= (2bc (b
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 3 - Solutions
1.* (a) See Figure 1: ABCD is a rectangle. The lines AB and CD are parallel: this
is because P AB = ADC = /2. Also t
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 7 - Solutions
1.* Let M be the midpoint of BC . Then
bc
.
,
22
As the hint says, we need to show that MA = MB = MC . We calculate
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 8 - Solutions
1. See Figure 1. As the hint says, we take M the midpoint of the line segment BC .
The complex number corresponding
University of Regina
Department of Mathematics and Statistics
MATH231 Euclidean Geometry Winter 2014
Homework Assignment No. 9 - Solutions
For each of the following quadratic curves do as follows:
(a) Decide whether it is an ellipse, hyperbola, or parabol