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1.12.10 Lesson Plan MYP: Congruence Introduction At the end of the day students will…know why the base angles of an isosceles triangle are congruent, understand postulates for SSS, ASA, SAS congruence and use them to prove other properties/theorems Standards Taught… Using properties of triangles to solve problems Identifying patterns Anticipation of next steps… Properties of quadrilaterals E 40º Warm-Up… Find the measure of angles D and C D C Step by step instructions… Discussion: A triangle is the most simple and elegant of shapes. Because they are so simple they are powerful. All formulas for area (Including a circle), indirect measurement, trigonometry, GPS technology, navigation are all based on the simple properties of triangles. (5 minutes) Congruence definition: If all three corresponding sides and all three corresponding angles are congruent then the triangles are congruent Congruence notation. Discuss the importance of order. Discuss postulates and talk about how we use these postulates to prove various things about congruent triangles. Later in the lesson we will use the postulates to prove why the base angles of an isoscles triangle are congruent. Postulates are shortcuts to knowing that triangles are congruent. For instance to be congruent means that all angles and all sides are the same however we can deduce that two triangles are congruent if we are given enough information. Are the triangles congruent? To say yes we could physically measure all angles and the sides or if we just measure a few things it ought to be enough to say they are congruent. Example: We know they are congruent without measuring the angles because of SSS. Discuss each of the others SAS and ASA. Discuss why AAA and SSA don’t work as congruence shortcuts. Discuss how AAS is just ASA because if 2 angles in a triangle are congruent then third must be as well. Lesson joke: If it smells like SSA then it is SSA. Lesson Question: Why are the base angles of an isosceles triangle congruent? Prove: Why the base angles of an isosceles triangle are congruent. B A C Demo how to write a proof 1. Use sketchpad as an inductive proof. (10 minutes, this is optional) 2. Locking a triangle with SAS postulate 3. Have the students vote on SSS, ASA, SSA, AAA. (15 minutes) 4. Practice problems from page 124 classroom exercises. Classwork/Homework: Read section 4 -1 in your book do problems 5-16. Write a paragraph proof that shows why the base angles of an isosceles triangle are congruent. The paragraph should look something like this: B A E C Triangle ABC is known to be isosceles. This tells us that AB BC . Next we bisect angle ABC forming two triangles. If we can prove these triangles are congruent then we can show that the base angles are also congruent. First show angle CBE congruent to angle ABE because we bisected them then they share BE therefore through SAS they are congruent and by extension angles A and C are also congruent. Have students write a paragraph proof and share it with their group then have a couple students write their proof on an overhead and present to the class. Plan for independent practice… Classwork or homework: Page 137 # 1-8. Page 124125 written exercises # 1 – 15.