Download File - Geometry

Ch. 4 Review
Direct Lesson
Topic: Chapter 4 Review
Duration: 90 minutes
Materials: Proof Packet, Chapter 4 Review, textbook.
Michigan State Standards/Benchmarks:
L3.1.3 Define and explain the roles of axioms (postulates), definitions, theorems, counterexamples, and
proofs in the logical structure of mathematics. Identify and give examples of each.
L3.3.1 Know the basic structure for the proof of an “If…, then…” statement. Use the fact, in
mathematical and everyday settings, that the contrapositive is logically equivalent to the original while
the inverse and convers are not.
G1.1.1 Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles,
supplementary angles, complementary angles, and right angles.
G1.1.2 Solve multistep problems and construct proofs involving corresponding angles, alternate interior
angles, alternate exterior angles, and same-side (consecutive) interior angles.
G1.1.4 Given a line and a point, construct a line through the point that is parallel to the original line
using a straightedge and compass. Given a line and a point, construct a line through the point that is
perpendicular to the original line. Justify the steps of the constructions.
G1.2.1 Prove that the angles sum of a triangle is 180⁰ and that an exterior angle of a triangle is the sum
of the remote interior angles.
G1.2.2 Construct and justify arguments and solve multistep problems involving angle measure, side
length, perimeter, and areas of all types of triangles.
G1.2.4 Prove and use the relationships among the side lengths and the angles of 30-60-90 triangles and
45-45-90 triangles.
G1.2.5 Solve multistep problems and construct proofs about the properties of medians, altitudes and
perpendicular bisectors to the sides of a triangle, and the angles bisectors of a triangle. Using a
straightedge and compass, construct these lines.
G2.3.1 Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria and that right
triangles are congruent using the hypotenuse-leg criterion.
G2.3.2 Use theorems about congruent triangles to prove additional theorems and solve problems, with
and without use of coordinates.
Objectives:
SWBAT:
- Classify triangles by sides and by angles.
- Create a proof of the Triangle Sum Theorem.
- Create a proof of the Exterior Angles Theorem.
- Identify corresponding parts of congruent triangles.
- Determine triangle congruence using SSS, SAS, ASA, and AAS congruence theorems given two
triangles.
- List corresponding angles and sides between congruent triangles.
- Create proofs to show triangle congruence.
- Use properties of isosceles and equilateral triangles to show angle measures, side lengths, and
prove triangle congruence.
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Use properties of right triangles to show angle measures, side lengths, and prove triangle
congruence.
Prove triangle congruence using the Hypotenuse-Leg (HL) Theorem.
Use the fact that corresponding parts of congruent triangles are congruent to prove information
beyond triangle congruence.
Purpose:
In math, we are usually given the question and need to figure out the answer. In geometry, however, we
are given the question and the answer and are asked why the answer is what it is. This chapter is very
proof-heavy, and it is good practice to show triangle congruence. It is an integral chapter in this course
because it really pushes forth the importance of reasoning and critical thinking.
Anticipatory Set:
Ask students to create a brainstorming session of all the things we have talked about in this chapter like
corresponding parts, congruence, congruence theorems and postulates, coordinate proofs, etc. This way
they can kick-start their brains into thinking about the review.
Input:
After reviewing the proof packet due today, students will have time to work on their review in class. If
they have questions, I will be there to clarify. If they do not finish, it will be homework. See attached
review.
Modeling:
We will go over the proof packet together. If I notice that many of the students are asking about the
same question, I will get them started.
Checking for Understanding:
I will be roaming the room to see how students are doing. They can stop me, and often do, as I walk
around.
Guided Practice:
By working on the review in class, they will have a chance for clarification.
Closure:
Students will be reminded of the test next class, so they need to study and practice as many proofs as
possible. They can find extra practice proofs in their books.
Independent Practice/Assessment:
Complete the review at home and study.
Adaptations/Differentiations:
Students with accommodations and/or IEPs have additional time to complete the assignment.
Depending on their plan, they may have up to 2 additional class periods to turn it in.