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Transcript

Geometry – Erlin Fall 2012 SKILL TRI 01 TRI 02 TRI 03 TRI 04 TRI 05 TRI 06 TRI 07 TRI 08 TRI 09 TRI 10 TRI 11 TRI 12 TRI 13 TRI 14 TRI 15 TRI 16 TRI 50 TRI (Triangles) Unit DESCRIPTION Define and classify triangles by sides and angles. Fill in the missing statements/reasons in a 2 column proof of the Triangle Angle Sum Theorem. Given two angles of a triangle, find the third. Given algebraic expressions for the three angles in a triangle, solve for x and find the measure of each angle. Be able to provide the steps necessary to write a Proof by Contradiction. State the corollaries to the Triangle Angle Sum Theorem a) In a triangle, no more than one angle can be greater than or equal to 90 degrees. (this is a proof by contradiction). b) In a right triangle, the two non-right angles are complementary. c) If two angles of one triangle are congruent to two angles of another, then the third angles are also congruent. State and apply the Remote Interior Angles Theorem. Solve problems, given exterior and remote interior angles, using algebra. Define polygon congruence. Given two polygons, determine if they are congruent. Given two congruent polygons (especially triangles), write polygon congruence statement and identify congruent corresponding parts. Use SSS, SAS, ASA, AAS, RHL to determine if 2 triangles are congruent. Write two column proofs to establish simple triangle congruence. Write flow proofs establishing congruence of triangles. Write two column or flow proofs for more complicated triangle congruence (including Reflexive, Symmetric, Parallel Lines, Vertical Angles, CPCTC, etc.). Prove Isosceles Triangle Theorem in each of four ways: Given an isosceles triangle and ONE of the following: altitude, angle bisector or median, prove that base angles are congruent. Prove the Converse of the Isosceles Triangle Theorem. Apply the concepts of Isosceles Triangle Theorem and its Converse in solving algebraic equations. Given a triangle and designated parts, construct significant segments. a) Given a triangle and a designated vertex, construct the median. b) Given a triangle and a designated vertex, construct the altitude. c) Given a triangle and a designated vertex, construct the angle bisector. d) Given a triangle & a designated side, construct perpendicular bisector. TRI 99 Solve problems you haven’t seen before, using analysis and synthesis of the information learned so far. TriAgain1 Use Triangle Inequality Theorem to determine if three given sides form a triangle. Also be able to determine the range of values for a third side, given the other two. TriAgain2 Given two angles in a scalene triangle, list the triangle’s side lengths in descending order and vice versa. TriAgain50 Given a triangle construct the Centroid. Describe its significance. TriAgain51 Given a triangle construct the Incenter. Demonstrate its significance. TriAgain52 Given a triangle construct the Circumcenter. Demonstrate its significance. Assignment #20: TRI 01, 02 p. 173 #5-7; p. 114 #34-37 & worksheet & sketch a scalene, acute, obtuse, right, isosceles Triangle MASTERY