MAFS.912.GCO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems. (Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.)
MAFS.912.GCO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. (Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.)

• identify and use the properties of congruence and equality (reflexive, symmetric, transitive) in my proofs. • interpret geometric diagrams and identifying what can and cannot be assumed. • apply theorems, postulates, (including angle addition) or definitions to prove theorems about lines and angles. • define complementary and supplementary angles.
• classify triangles by sides and angles. • prove theorems about triangles. • solve problems using definitions, theorems, postulates, about triangles, including: a) Measures of interior angles of a triangle sum to 180; b) Base angles of isosceles triangles are congruent; c) An exterior angle of a triangle is equal to the sum of the measures of the remote interior angles

Monday (2nd Period) / Tuesday (7th & 8th Periods)
Bellringer
Review Bellringer
Lecture on Reasoning and Proof. The objective is to learn to:
 To make conjectures based on inductive reasoning.
 Find counterexamples.
 To determine truth values of negations, conjunctions, and disjunctions.
 Represent conjunctions and disjunctions using Venn diagrams.
 To analyze statements in ifthen form.
 Write the converse, inverse, and contrapositive of ifthen statements.
 Learn about biconditional statements.
 Use the Law of Detachment.
 Use the Law of Syllogism
Exit Ticket – Review covered material and report how comfortable are with what lectured on today.
Homework:
 43 Study Guide and Intervention Congruent Triangles Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
 44 Study Guide and Intervention Proving Congruence – SSS, SAS Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
 45 Study Guide and Intervention Proving Congruence – ASA, AAS Worksheets – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
Wednesday (2nd, 7th & 8th Periods)
Bellringer
Review Bellringer.
Review lecture notes from Monday/ Tuesday. Go over examples of basic postulates about points, lines and planes and to write paragraph proofs.
Exit Ticket – Review covered material and report how comfortable are with what lectured on today.
Thursday (2nd Period) / Friday (7th & 8th Periods)
Bellringer
Review Bellringer
Lecture – Postulates and Proofs. The objective is to learn to:
 Identify and use basic postulates about points, lines, and planes.
 Write paragraph proofs.
 Use algebra to write twocolumn proofs.
 Use properties of equality to write geometric proofs.
 Write proofs involving segment addition.
 Write proofs involving segment congruence.
 Write proofs involving supplementary and complementary angles.
 Write proofs involving congruent and right angles.
Exit Ticket – Review covered material and report how comfortable are with what lectured on today.
Homework (graded assignments – formative):
 25 Study Guide and Intervention Postulates and Paragraph Proofs Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
 26 Study Guide and Intervention Algebraic Proof Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
 27 Study Guide and Intervention Proving Segment Relationships Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
 28 Study Guide and Intervention Proving Angle Relationships Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)

Summative
None
Formative
 Bellringers – due 15 minutes after class starts
 Exit Tickets – due at the end of class
 43 Study Guide and Intervention Congruent Triangles Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
 44 Study Guide and Intervention Proving Congruence – SSS, SAS Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
 45 Study Guide and Intervention Proving Congruence – ASA, AAS Worksheets – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)

For help, please refer to lecture notes and/or practice on IXL www.ixl.com (not for a grade) the following tasks:
 C.8 Proofs involving angles
 D.6 Proofs involving parallel lines I
 D.7 Proofs involving parallel lines II
 K.7 Proving triangles congruent by SSS, SAS, ASA, and AAS.
 K.8 Proofs involving corresponding parts of congruent triangles
