Lesson Standards/Objective(s):  What mathematical skill(s) and understanding(s) will be developed? Which Mathematical Practices do you expect students to engage in during the lesson?

G.SRT.A.3 Use properties of similarity transformations to establish the AA criterion for two triangles to be similar.

MP2:  Reason abstractly and quantitatively.

MP3:  Construct viable arguments and critique the reasoning of others.

MP6:  Attend to precision.

MP8:  Look for and express regularity in repeated reasoning.

 

Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson?

Have students use the Frayer Model Similar Figures graphic organizer to recall the definition and properties of Triangle Similarity, giving examples/non-examples to illustrate the meaning.

Lesson Closure Notes:  Exactly what summary activity, questions, and discussion will close the lesson and connect big ideas? List the questions. Provide a foreshadowing of tomorrow.

1.         State AA Rule in your own words.

2.         Solve for x, y, and z in the triangles given. (See Frayer Model document, page 2.)

 

Lesson Tasks, Problems, and Activities (attach resource sheets):  What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices.

1.         Place students in small groups of four.  Have each group draw a large Triangle ABC with side lengths of their choosing on a coordinate plane using graph paper. (You may want to have some groups draw a right triangle, some an acute triangle, and others an obtuse one.)

2.         Tell each student to copy their group’s triangle onto a sheet of patty paper and label vertices A, B, and C so they all have congruent copies of Triangle ABC. (MP6)

3.         Using another sheet of patty paper, have each student draw a line segment with a length exactly ˝ of BC and label the segment endpoints E and F. (They can easily find this length by folding the patty paper to bisect side BC.)

4.         Ask students to copy angle B from the original triangle onto the new line segment at endpoint E and copy angle C from the original triangle onto the line segment at endpoint F. Have them extend the sides to form a new triangle DEF and mark the triangles to indicate that angle B is congruent to angle E and angle C is congruent to angle F.  (A sample is provided in the Patty Paper Sample Triangle for AA Similarity.)

5.         Tell students to compare their new triangle (DEF) to the original one they copied (ABC) as well as to those drawn by others in their group. They will do this by placing the smaller triangle on top of the other, making observations and conclusions about how the measures of corresponding angles and sides compare as they slide it around. Have students compare observations and conclusions with other groups to identify key findings (Look for evidence of MP3, MP8.)

6.         Have students write congruency and/or equality statements about the measures of corresponding angles and sides for Triangles ABC and DEF on one of their sheets of patty paper. If you prefer, students can place the patty paper containing Triangle DEF on the coordinate plane used to draw triangle ABC originally and assign coordinates to the vertices of DEF to determine its side lengths exactly or to determine the ratio of the side lengths. (Look for evidence of MP2.)

7.         Debrief this activity and have students make conjectures by asking, “Can we conclude that Triangles ABC and DEF are similar triangles? How do you know? Do you think the triangles would be similar if the sides of Triangle DEF were each 1/3 the length of the corresponding sides of Triangle ABC? How much information (which parts) did we use from the original triangle to draw one similar to it? Is this enough information to conclude that the triangles are similar in all cases (knowing two angles of one triangle are congruent to two angles of another triangle)?” (Look for evidence of MP3, MP8.)

8.         Have students identify this as the AA Criterion and summarize it in their own words.

 

Evidence of Success:  What exactly do I expect students to be able to do by the end of the lesson, and how will I measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding.

By the end of the lesson, students should be able to state the AA criterion for two triangles to be similar and provide supporting examples and justification to prove it that it holds true for all types of triangles (acute, obtuse, and right).

 

Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc

Vocabulary: similar triangles, corresponding sides, corresponding angles, proportional, congruent

 

Resources:  What materials or resources are essential for students to successfully complete the lesson tasks or activities?

Graph Paper

Straightedge

Patty Paper

Pencil

 

Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson?

 

Provide more practice with applications of the AA Similarity Rule like those in the closing activity.

Lesson Reflections:  How do you know that you were effective? What questions, connected to the lesson standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?

 

How well did these explorations help develop students’ conceptual understanding of the AA criteria for two triangles to be similar? How do you know?

Are students able to state and apply the criteria accurately?

Are students able to identify the criteria when presented in different applications?

Can all students apply the criteria in problem-solving situations?

What real world applications or extensions to learning can I introduce to help students make meaningful connections for this concept?

 

 

 

Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.