Starting Wednesday, bring a decent compass (that will lock its distance and not slip), a ruler, a protractor and a pair of scissors to class every day.
Write proofs for each of the follow problems. The sign = will be used to mean congruence when it (hopefully) will not lead to confusion.
1.1 - Suppose ABC is an isosceles triangle with AB = AC.
(a) If M is the midpoint of BC, prove that triangle AMB = triangle AMC.
(b) Based on what you just proved, what is the strongest statement you can make about angle AMB?
1.2 - Given a quadrilateral ABDC. Suppose AB = DB and AC = DC. Prove that angle BAC = angle BDC. Think carefully to include all cases.
(Such a 4-sided figure ABDC is called a kite .)
1.3 - The Fundamental Property of a Perpendicular Bisector
(a) Write the definition of the perpendicular bisector of a segment.
(b) If AB is a segment and P is any point on the perpendicular bisector of AB, prove that the triangle PAB is isosceles (with PA = PB).
(c) If a triangle PAB is isosceles (with PA = PB), prove that P is a point on the perpendicular bisector of AB.
1.4 - Given the kite ABDC in problem 1.2,
(a) prove that line BC is the perpendicular bisector of segment AD.
(b) prove that ray BC bisects angle ABD and ray CB bisects angle DCA.
1.5 - Berele-Goldman, Problem 1.2. (Hint: this is related to Problem 1.2.)
1.6 - Berele-Goldman, Problem 1.3.
1.7 - Berele-Goldman, Problem 1.7. Do the constructions with compass and unmarked straightedge.