Quarter 2, Week 1: October 16th – 20th

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TeacherFelicia Taylor
Subject AreaGeometry Honors
Grade Level8
Week #10
Unit of InstructionUnit 2A: Triangle Congruence and Proofs
Standard(s) Taught

MAFS.912.G-CO.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.G-CO.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.)

Learning Targets and Learning Criteria

• 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

Classroom Activities

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 if-then form.
  • Write the converse, inverse, and contrapositive of if-then 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:

  1. 4-3 Study Guide and Intervention Congruent Triangles Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
  2. 4-4 Study Guide and Intervention Proving Congruence – SSS, SAS Worksheet –  due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
  3. 4-5 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 two-column 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):

  1. 2-5 Study Guide and Intervention Postulates and Paragraph Proofs Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
  2. 2-6 Study Guide and Intervention Algebraic Proof Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
  3. 2-7 Study Guide and Intervention Proving Segment Relationships Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
  4. 2-8 Study Guide and Intervention Proving Angle Relationships Worksheet – due Monday, October 23rd (2nd Period class) / due Tuesday, October 24th (7th & 8th Period classes)
Assignments Due

Summative

None

Formative

  1.  Bellringers – due 15 minutes after class starts
  2. Exit Tickets – due at the end of class
  3. 4-3 Study Guide and Intervention Congruent Triangles Worksheet – due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
  4. 4-4 Study Guide and Intervention Proving Congruence – SSS, SAS Worksheet –  due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
  5. 4-5 Study Guide and Intervention Proving Congruence – ASA, AAS Worksheets –  due Wednesday, October 18th (2nd Period) / due Thursday, October 19th (7th & 8th Periods)
Additional Resources

For help, please refer to lecture notes and/or practice on IXL www.ixl.com  (not for a grade) the following tasks:

  1. C.8 Proofs involving angles
  2. D.6 Proofs involving parallel lines I
  3. D.7 Proofs involving parallel lines II
  4. K.7 Proving triangles congruent by SSS, SAS, ASA, and AAS.
  5. K.8 Proofs involving corresponding parts of congruent triangles