L3+O'Halloran,Erin+Marissa


 * UNIVERSITY OF MAINE AT FARMINGTON**
 * COLLEGE OF EDUCATION, HEALTH AND REHABILITATION**
 * LESSON PLAN FORMAT**


 * Teacher’s Name:** Ms. Erin O'Halloran **Lesson:** 3
 * Grade Level:** 10 **Topic:** Similar and Congruent Polygons

__**Objectives**__
Student will understand that computing areas and volumes is based on the object's properties and dimension. Student will know similarity, congruence, SAS, AAS, AAA, SSS, complimentary angles, supplementary angles, corresponding angles, alternate interior angles, alternate exterior angles, vertical angles, linear pair angles, exterior angles theorem. Student will be able to use similarities and congruence on polygons to determine certain properties.

__**Maine Learning Results Alignment**__
//Geometric Figures// //Grades 9 - Diploma// //Students justify statements about polygons and solve problems// **
 * //Maine Learning Results: Mathematics- C. Geometry//


 * Rationale:** Using the theory of congruence and similarity, students will be able to solve problems using properties of polygons. Areas and volumes can be determined using these similarities and congruences.

__**Assessment**__
Students will have to make a complete a graphic organizer to organize all the different angles and congruence theorems. There will be plenty of time in class to organize their thoughts while they take notes. Once students have the information organized, they will be split into groups and compare notes. If one of the students missed anything, they can gather what they missed from another student in their group. After students have had a chance to create their organizers, the teacher will go around and inspect the neatness of the graphic organizer.
 * Formative (Assessment for Learning)**

Students will create an infomercial about similarities and congruence and how every household should have one. They will need to sell the "congruence" or "similarity" to an audience. In order to catch the audience's attention, the presenters will need to explain what each term means. Examples and properties of the terms need to be mentioned in the infomercial. Students need to be creative, using what the iMovie program offers. The finished product will be presented in class. Congruence and similarity needs to be mentioned in the final product along with two angle congruence properties and two triangle congruence theorems.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology**: Students will use iMovie or Windows Movie Maker to create the finished infomercial. They will need to record themselves using a video camera, camera, or webcam. Using clips from youtube or any other video website is permitted as long as the videos are properly sited.


 * Social Studies**: In many types of architecture, similar triangles and congruent triangles. This does not only appeal to the eye, but structurally, it makes sense that similar polygons would be used. Even in maps, the scales are examples of similar sides.

__Groupings__
For the formative assessment, students will be put into the Jigsaw grouping. One student will go through all the properties of similarity, one student will go through all the triangle congruence theorems, one student will go through the different angle congruence theorems. The other students in the group will go through their graphic organizers and make sure they have the each of the theorems and definitions.

__**Differentiated Instruction**__

 * Strategies:**
 * Linguistic**: Have students write out a script to show what each person in the infomercial is saying. The script can be shown to the teacher to make sure that the properties are correct or if there is enough information being mentioned.
 * Intrapersonal**: Put aside time in class to work on the project quietly by themselves. Students will have an entire class period to meet with their partner(s) and will be able to use materials in the school to incorporate into their infomercial.
 * Interpersonal**: Students will work in groups and can collaborate on the script and effects that will be put into the infomercial. Ideally, there will be at least 3 students in a group and together they can create the script and film the infomercial.
 * Naturalist**: Find similarities and congruence in nature, like the sizes of trees, congruence of the shapes of leaves, etc. This could be part of the infomercial that would grab the attention of the audience.
 * Musical**: Have students create a rhyme to remember the what makes two polygons similar. Putting the rhyme into the infomercial could grab the audience's attention and would be a creative way to sell "similarity".
 * Logical**: Students would show each step of the how we know two elements are congruent and not skip any steps. Students can take a completely mathematical approach to the infomercial and do some examples of finding similar triangles or congruent angles/sides.

**//I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.//**
 * Modifications/Accommodations**

**Absent:** If students are absent, then they will need to get the notes about congruence and similarity from another student in the class. Should the absent student have a question, they can email the teacher and set up an appointment. If the student is absent during the in class work day, the absent student's partners will need to contact him/her and assign the student a job to finish with the project. If the group needs more time because of absent partners, depending on the situation, more time will be allotted. Students should still email the teacher when they know they are going to be absent.

To get students interested into the subject of similar or congruent triangles, students can experiment with this [|website]. The site has interactive triangles that change accordingly when students make sides/angles larger or smaller. By morphing the triangles into different shapes, students can generalize what would happen if the triangle were right, acute, or obtuse.
 * Extensions**

__**Materials, Resources and Technology**__
[|Congruence and Similarity]; defines similarity and congruence, SAS AAS SSS AAA, proportional sides. [|Congruent Angles]; defines angles such as: acute, obtuse, complementary, supplementary, vertical, alternate interior, alternate exterior, corresponding. [|Exterior Angle Theorem]; describes the exterior angle theorem and proves it.

__Source for Lesson Plan and Research__

 * LCD Projector
 * Computer to show software and slides
 * Text book
 * Hand outs
 * Graphic organizer
 * Web that lists the congruence and similarity theorems
 * Angles worksheet
 * Congruent triangles worksheet
 * Computers with iMovie or Windows Movie Maker
 * iMovie or Movie Maker tutorial

__**Maine Standards for Initial Teacher Certification and Rationale**__

 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//**
 * Rationale:**
 * Beach Ball**: Students will have the freedom to choose how to make congruence and similarity appealing to the audience. They can use a mixture of their partners MIs. The group could use different approaches using many different ideas.
 * Clipboard**: Using the graphic organizer, students will have a clear idea of what they need to incorporate into the final product. The expectations of introducing both similarity and congruence, having two triangle congruence theorems mentioned, and having two angle congruence theorems will be evident in the instructions.
 * Microscope**: Students will be able to discuss their ideas in the class with their group. Together they can learn and focus on details needed in the project.
 * Puppy**: Working in the classroom on computers will ensure a comfortable environment. Groups can bounce ideas off each other and there will be plenty of other people to talk to if the individuals in the group do not get along.

Refer to content notes to understand what students will know. //Student will be able to use similarities and congruence on polygons to determine certain properties.// In this lesson, students will learn about similarity and congruence between sides and angles. This knowledge would be extremely helpful in measurements in everyday life. Almost all comparisons of measurements are based on congruence and similarity. Making scales is a good example of the importance of similarity and proportions. Students will be able to apply these techniques to situations such as reading a map or determining measurements based on a scale or schematics.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:**


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * Rationale:**
 * Linguistic**: Have students write out a script to show what each person in the infomercial is saying. The script can be shown to the teacher to make sure that the properties are correct or if there is enough information being mentioned.
 * Intrapersonal**: Put aside time in class to work on the project quietly by themselves. Students will have an entire class period to meet with their partner(s) and will be able to use materials in the school to incorporate into their infomercial.
 * Interpersonal**: Students will work in groups and can collaborate on the script and effects that will be put into the infomercial. Ideally, there will be at least 3 students in a group and together they can create the script and film the infomercial.
 * Naturalist**: Find similarities and congruence in nature, like the sizes of trees, congruence of the shapes of leaves, etc. This could be part of the infomercial that would grab the attention of the audience.
 * Musical**: Have students create a rhyme to remember the what makes two polygons similar. Putting the rhyme into the infomercial could grab the audience's attention and would be a creative way to sell "similarity".
 * Logical**: Students would show each step of the how we know two elements are congruent and not skip any steps. Students can take a completely mathematical approach to the infomercial and do some examples of finding similar triangles or congruent angles/sides.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * Rationale:** Using both the formative and summative assessments assigned for this lesson, the teacher can determine if the students fully understand the different areas and volumes. Because the formative and summative assessments are using two different sides of the brain, students with different learning styles will be able to learn the way they want to.

Students will have to make a complete a graphic organizer to organize all the different angles and congruence theorems. There will be plenty of time in class to organize their thoughts while they take notes. Once students have the information organized, they will be split into groups and compare notes. If one of the students missed anything, they can gather what they missed from another student in their group. After students have had a chance to create their organizers, the teacher will go around and inspect the neatness of the graphic organizer.
 * Formative (Assessment for Learning)**

Students will create an infomercial about similarities and congruence and how every household should have one. They will need to sell the "congruence" or "similarity" to an audience. In order to catch the audience's attention, the presenters will need to explain what each term means. Examples and properties of the terms need to be mentioned in the infomercial. Students need to be creative, using what the iMovie program offers. The finished product will be presented in class. Congruence and similarity needs to be mentioned in the final product along with two angle congruence properties and two triangle congruence theorems.
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
For classroom arrangement, I will have students sit in a perimeter so they everyone can see the screen without other peoples' heads in the way. It is vital to see which polygon is being discussed during the lecture to minimize confusion. The notes for my class will be displayed from a computer using an LCD projector. Once it is time to work on the project in class, students will set their desks in groups so that they can easily communicate with the other people in the group.

similarity, congruence, SAS, AAS, AAA, SSS, complimentary angles, supplementary angles, corresponding angles, alternate interior angles, alternate exterior angles, vertical angles, linear pair angles, exterior angles theorem.

Day 1: Introduce congruence (10 minutes) Introduce similarity (10 minutes) Introduce corresponding angles (5 minutes) Introduce complimentary angles (5 minutes) Introduce supplementary angles (5 minutes) Introduce vertical angles (5 minutes) Introduce linear pair angles (5 minutes) Introduce alternate interior angle (5 minutes) Introduce alternate exterior angles (5 minutes) Introduce exterior angles theorem (5 minutes) Introduce project and assign groups for the project and have students ask questions (5 minutes) Pass out graphic organizers and have them work in Jigsaw groups for the rest of class (15 minutes)

Day 2: Introduce SAS (10 minutes) Introduce AAS (10 minutes) Introduce AAA (10 minutes) Introduce SSS (10 minutes) Have students work in their groups and have them think of a script for the rest of class (20 minutes) Work on worksheets in class and have students finish for homework. (20 minutes)

Day 3: Go over worksheets and homework. (20 minutes) Have students work on their projects working with their group and on the computer. (60 minutes)

Students will be able to determine similar triangles and congruent triangles.**//Students justify statements about polygons and solve problems//.** In this lesson, students will learn about similarity and congruence between sides and angles. This knowledge would be extremely helpful in measurements in everyday life. Almost all comparisons of measurements are based on congruence and similarity. Making scales is a good example of the importance of similarity and proportions. Students will be able to apply these techniques to situations such as reading a map or determining measurements based on a scale or schematics. Watch this [|rap] before starting the lesson to get students interested in the material. **Where, Why, What, Hook Tailors: Visual, Logical, Spatial**

Student will know similarity, congruence, SAS, AAS, AAA, SSS, complimentary angles, supplementary angles, corresponding angles, alternate interior angles, alternate exterior angles, vertical angles, linear pair angles, exterior angles theorem. Through many examples, students will be able to make the connection between congruent angles and similar sides. Worksheet will be assigned to students and as a class, we will go over the problems together. The teacher will also be able to see if students are comprehending the content by how organized their graphic organizers are. Given the Cluster Word Web, students will be able to make the connections between the similarities and congruences. Going through the Cluster Word Web will assure the teacher that the students are understanding the material at a higher level. **Equip, Explore, Rethink, Revise, Tailors: Linguistic, Interpersonal, Intrapersonal**

Student will be able to use similarities and congruence on polygons to determine certain properties. Given the Cluster Word Web, students will be able to make the connections between the similarities and congruences. Going through the Cluster Word Web will assure the teacher that the students are understanding the material at a higher level. By listening to the examples of similar and congruent sides and angles, the teacher will be able to assess if the students are understanding the content. The rest of the group will be able to hear other examples from other students if they need to better understand the material. While students are in the Jigsaw groups, one part of the group will master similarity and the other will master congruence. Once students have done enough examples of the material they were assigned, they will need to explain the concept to the rest of the group. The teacher will see the evidence of learning by how confident the students explaining their concept is. **Explore, Experience, Revise, Refine, Tailors: Linguistic, Logical, Visual**

Students will be given a self assessment sheet where they will have to describe how well the group worked together and how much of the project they did. What did students decide to relate to congruence and similarity in order to capture the audience? Can congruence and similarity be related to that theme? The teacher will assess grade the group as a whole. The grade will reflect the creativity of the infomercial and the correctness of the content. This lesson relates to the next lessons because students can relate area and volume. **Evaluate, Tailors: Intrapersonal**

=Congruent Angles=
 * Content Notes**

An acute angle is an angle measuring between 0 and 90 degrees. Example: The following angles are all acute angles.

An obtuse angle is an angle measuring between 90 and 180 degrees. Example: The following angles are all obtuse.

A right angle is an angle measuring 90 degrees. Two lines or line segments that meet at a right angle are said to be perpendicular. Note that any two right angles are supplementary angles (a right angle is its own angle supplement). Example: The following angles are both right angles.

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. One of the complementary angles is said to be the complement of the other. Example: These two angles are complementary. Note that these two angles can be "pasted" together to form a right angle!

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. One of the supplementary angles is said to be the supplement of the other. Example: These two angles are supplementary. Note that these two angles can be "pasted" together to form a straight line!

For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Vertical angles have the same degree measurement. Angle BEC and angle AED are also vertical angles.

For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle D are called alternate interior angles. Alternate interior angles have the same degree measurement. Angle B and angle C are also alternate interior angles.

For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle D are called alternate exterior angles. Alternate exterior angles have the same degree measurement. Angle B and angle C are also alternate exterior angles.

For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle C are called corresponding angles. Corresponding angles have the same degree measurement. Angle B and angle D are also corresponding angles. = Similar Triangles = **Similar triangles** have the same shape, but the size may be different. Remember " @ " means "is congruent to" and "~" is "similar to". Examples a/f = b/d = c/e = **factor** || <B @ <D <C @ <E || a/f = 6/3 = **2** b/d = 8/4 = **2** c/e = 10/5 = **2** || <B @ <D <C @ <E || a/f = 3/3 = **1** b/d = 4/4 = **1** c/e = 5/5 = **1** || Two triangles are similar if: Notice the corresponding angles for the two triangles in the applet are the same. The corresponding sides lengths are the same only when the scale factor slider is set at 1.0. Study the side lengths closely and you will find that the corresponding sides are proportional. = =
 * **Corresponding Triangles** || **Corresponding Congruent Angles** || **Corresponding Proportional Sides**
 * D ABC ~ D FDE || <A @ <F
 * D ABC @ D FDE || <A @ <F
 * two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent).
 * the three pairs of corresponding sides are proportional.

=Triangle Congruence=


 * __SSS__ **

**//If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent.//**

**__ASA__**

//**If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.**// **__SAS__**

**//If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent.//** **__AAS__**

//**If two angles and a non included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the two triangles are congruent.**//

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. Proof:
 * Given:** ∆//PQR//
 * To Prove:** [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image001.gif align="absmiddle"]]
 * || **Statement** || **Reason** ||
 * 1 || ∆//PQR// is a triangle || Given ||
 * 2 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image003.gif]] || Triangle Sum Theorem ||
 * 3 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image004.gif]] form a linear pair || Definition of linear pair. ||
 * 4 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image004.gif]] are supplementary || If two angles from a linear pair, they are supplementary. ||
 * 5 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image005.gif]] || Definition of supplementary angles. ||
 * 6 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image006.gif]] || Statements 2, 5 and Substitution Property. ||
 * 7 || [[image:http://hotmath.com/hotmath_help/topics/exterior-angle-theorem/exterior-angle-theorem-image007.gif]] || Subtraction Property. ||

[|Angles Worksheet] [|iMovie Tutorial]
 * Handouts**