Be able to state the definition and to use the following terms:
Midpoint, Median, Perpendicular Bisector, Angle Bisector, Exterior Angle Bisector, Circumcenter, Circumcircle, Incenter, Incircle, Ecircle (same as Excircle), Altitude, Area, Quadrilateral, Trapezoid, Parallelogram, Rhombus, Rectangle, Square.
Be able to state the use the following theorems:
SAS, ASA, SSS, HL (= SSA for right triangles) for both congruence and similarity.
Basic properties of isosceles triangles and kites. Locus Theorem for Perpendicular Bisectors and Angle Bisectors. Triangle inequality and other inequalities from BG. Statements about quadrilaterals equivalent to definition of parallelogram. Statements about quadrilaterals equivalent to definition of rhombus.
Prove that the sum of the angles of a triangle is equal to a straight angle.
Review BG problems 2.2, 2.3, 2.4.
State and prove the area formula for a trapezoid.
Given two non-parallel "strips" of width d (i.e., parallel lines m1 and m2 at distance d from each another and another pair of lines n1 and n2, not parallel to m1 and m2, at distance d from each other), prove that the four lines are the (extended) sides of a rhombus.
Prove that the perpendicular bisector of any chord of a circle passes through the center of the circle. (Note: make this short by quoting big theorems.)
Prove that the perpendicular bisectors of the sides of a triangle are concurrent.
Prove that exactly one circle can be circumscribed about any triangle.
Given 3 lines which are the extended sides of a triangle, prove that there are exactly 4 points equidistant from each of these lines. (What does "equidistant from each of these lines" mean?) How is this related to tangent circles?
Prove that the angle bisectors of a triangle are concurrent.
Prove that exactly one circle can be inscribed in any triangle.
Prove that any two exterior angle bisectors of a triangle are concurrent with the (interior) angle bisector of the other angle.
Outline an area proof of the Pythagorean Theorem.
Given a line and a point A not on the line, construct a circle with center A which is tangent to the line.
Given two lines and a point B on one of the lines (but not on both), construct a circle through B which is tangent to both lines.
Let R be a rectangle with sides a and b. Given a figure with the rectangle R and a segment of length c, construct a rectangle S with one side = c and area S = area R. Hint: BG 3.3.
Given a triangle ABC, construct the circumcircle of ABC.
Given a triangle ABC, construct the incircle of ABC.
Given a triangle ABC, construct the ecircles (exscribed circles) of ABC.
Use a unmarked two-sided ruler to construct the interior and exterior angle bisectors of angle ABC.
In a "nice" case, show how to decompose a rectangle into a parallelogram of the same area but with one side = 1. Also, how to decompose a parallelogram with side 1 into a rectangle with same area.