|HW due on||Sections to read||Homework problems||Comments|
|September 14||Chapter 1 + lecture notes.|| 1.2.3, 1.3.3, 1.3.5, 1.4.3, 1.4.4|
I. Given a circle, construct the center of this circle
II. Given a circle C and points A and B, construct a point on C equidistant from A and B. Is there only one such point?
III. Construct a right isosceles triangle circumscribed around a given circle.
IV. Given a circle and a line, construct a tangent line to the circle parallel to the given line.
V. Given a circle, construct an inscribed rectangle such that the angle between its diagonals is 30 degrees.
Euclid's Elements: An interactive web-based version of the famous "Elements".
|September 21||Chapter 2 + lecture notes.|| 2.2.2, 2.3.1, 2.3.2, 2.3.3, 2.5.2, 2.7.5 |
I. Let A be a point outside a circle. Draw lines AX, AY tangent to the circle at X and Y. Prove that AX=AY.
II. Let ABCD be a quadrilateral such that angles ACB and ADB are equal. Show that all vertices of this quadrilateral lie on a circle.
III. Prove that every triangle has an inscribed circle and that the center of that circle is the intersection point of all three angle bisectors of angles of the triangle.
IV. Prove that every triangle has a circumscribed circle and that the center of that circle is the intersection point of all three perpendicular bisectors of sides of the triangle.
|October 3||Lecture notes||Some of the 15 problems in this worksheet are simple and some could be a bit tricky. Choose and solve 6 problems from the worksheet. (So different students can solve different subsets). You are welcome to try all problems but you are not allowed to submit more than 6. All of them will be graded.|| Quiz on September 28. |
Review of Euclidean geometry on October 3.
Midterm on October 5. Solutions for midterm.
|October 12||Chapter 3 (3.1-3.5).|| 3.2.4, 3.2.5, 3.2.6, 3.4.1, 3.4.2, 3.4.3, 3.5.1, 3.5.2|
I. A quadrilateral ABCD has vertices given by intersection points of lines y=kx+b, y=kx-b, y=mx+b and y=mx-b. Find coordinates of the intersection point of diagonals of the quadrilateral ABCD.
II. The line y=kx+k+1 (with k>0) intersects coordinate axes at points A and B. Find the smallest possible area of the triangle ABO (where O is the origin).
|October 19||Chapter 3 (3.6-3.8) + lecture notes.|| 3.6.1, 3.6.2, 3.6.3, 3.7.1, 3.7.2, 3.7.3|
I. Prove that every isometry of the plane takes circles to circles.
II. Suppose circles S1 and S2 of the same radius R intersect at points A and B. Let M and N be intersection points of S1 and S2 with the perpendicular bisector of the segment AB. Suppose, in addition, that M and N lie on the same side of the line AB. Prove: AB2+MN2=4R2.
III. Suppose a quadrilateral has an axis of symmetry. Show that either this quadrilateral is a trapezoid or the axis of symmetry is a diagonal of the quadrilateral.
IV. Construct an equilateral triangle with vertices on three given parallel lines.
|October 26||Chapter 4 + lecture notes.||TBA||Quiz on October 24.|
|November 2||Chapter 5+ lecture notes.||TBA|
|November 9||No reading assignment||No HW due|| Review of analytic geometry on November 7.|
Midterm on November 9
|November 16||Chapter 6 + lecture notes.||TBA|
|November 30||Chapter 7 + lecture notes.||TBA|
|December 7||Lecture notes.||TBA||Final Exam Review on December 12|