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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.