Similarity and Congruence of Triangles and Quadrilaterals

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```					 Similarity and Congruence of Triangles and
Author: Ruth Ingerly
Revision Date of Lesson Plan: 4-19-11

Overall Goal for the Lesson:
The students will apply the properties of similar triangles, similar quadrilaterals and
congruent triangles to solve problems and also determine unknown values by using these
properties.

Description of classroom, grade level, and students:

It will be a math classroom of 9th and 10th graders who have discussed the concepts of
similarity and congruence and have used deductive proofs to prove the properties of
similar and congruent triangles to be true.

Student Objectives for the lesson.

Given two geometric quadrilaterals, SWBAT determine unknown values on any given
problem using the properties of similarity.

Given two geometric triangles students will be able to state whether the shapes are
similar, congruent or neither with an accuracy of 8 out of 10 by using properties of
similar and congruent triangles.

Given two triangles, either similar or congruent, students will be able to determine
unknown values on any given problem using the properties of similarity and congruence.

Length of Lesson:

Two class periods. One day spent on similarity and one say spent on congruence.

Schedule of Activities:
Day 1: Similarity

We have been talking about similarity and congruence. A SMART Notebook lesson has
been planned in advance that uses different shapes and tools to talk about Similarity.

Teacher will walk students through how you can determine if two triangles are similar
through ratios. And then provide a few example on the board for the students to work
and figure out.
Students will be interactive in this lesson by answering questions that are prompted by
the teacher. Students will then explain to the class how they came to their conclusion and
the class will decide if their conclusion is correct or not.

Teacher will then introduce the idea or using the properties of similar triangles to find
missing information. Prompts students if they have any ideas.

Teacher puts an example on the board and asks the students to solve for x. Waits for
students to answer. (students must raise hands to answer) A student is chosen who will
go to the board and answer the question for the class. (what does the class think? Is the
student correct?)

What about for other shapes? Do you think that the same method will work in
determining similarity? Let’s look at quadrilaterals…

Teacher does similar method with quadrilaterals as with triangles.

At the end of the day there will be a short homework assignment that involves finding
missing information from similar triangles and determining if triangles are similar
(problems from the text or possibly a worksheet)

Day 2. Congruence

Introduce by asking what is the difference between similar figures and congruent figures.

Teacher review the properties of congruent triangles such as SAS or ASA etc with the
class. Teacher will then provide some example and ask the students if the figures are
congruent and why?

Like in the similarity lesson students will be interactive by coming to conclusions on their
own and having class discussions on whether they are correct or not.

“Yesterday when we talked about similarity we talked about using the properties of
similarity to solve for an unknown. Do you think that is also possible with congruent
figures?”

Teacher puts an example on the board and asks the students to solve for x. Waits for
students to answer. (students must raise hands to answer) A student is chosen who will
go to the board and answer the question for the class. (what does the class think? Is the
student correct?)

At the end of the lecture student are given a more extensive worksheet that combines
both similar and congruent figues.

A quiz can be given at the end of the week to insure that all students are understanding.
4. Similarity
b. Use ratios of similar 2-dimensional figures to determine unknown values, such as
angles, side lengths, perimeter or circumference, and area.

5. Congruence
b. Use the relationships of congruency of 2-dimensional figures to determine unknown
values, such as angles, side lengths, perimeter or circumference, and area.

PASS Instructional Technology Standards
Standard 3: The student will demonstrate knowledge of technology productivity
tools.
1. Use content-specific tools, software, and simulations (e.g., environmental probes,
graphing calculators, exploratory environments, Web tools) to support learning and
research.
2. Apply productivity/multimedia tools and peripherals to support personal productivity,
group collaboration, and learning throughout the curriculum.

Assessments: How will these activities be assessed?

Students will be required to participate in class for part of the assessment. At the end of
the lesson the students will be given a worksheet that combines similar and congruent
figures. Quiz will be given on the properties of congruent triangles (eg. SAS, ASA,
AAS, SSS) and similar triangles (proportions of sides and angles.)

Accommodations: How might the lesson need to be adapted for students with special
needs?

If a student has a vision impairment the teacher can provide the student with an enlarged
handout of the smart board presentation and activities.

Materials Needed:
Smart board activity
Paper
Pencil
Worksheets

Description and Rationale:
This lesson on Symmetry and Congruence address the OK PASS standards 4.b. and 5.b.
In this lesson we go over the main ways to tell if a shape (mostly triangles) is similar
and/or congruent. The lesson discusses how to use properties of lines and shapes to find
information about the length of different sides, the similarity ratio, and the angle
measurements of different triangles. This lesson is interactive and allows for students to
use their existing knowledge to help them discover for themselves the relationships
between similar and congruent triangles.

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