Download Sec4-2 Lesson Plan - epawelka-math

Elizabeth Pawelka
Triangle Congruence (SSS and SAS)
2/24/12 p.1
Geometry
Lesson Plans
Section 4-2: Triangle Congruence by SSS and SAS
2/24/12
Statement of Objectives
The student will be able to…
 prove triangles congruent using the SSS and SAS Postulates
Warm-up and Review of Homework (25 minutes)
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Warm-up, practice book p. 40, 1-10 (answers on sheet) (10 minutes)
They do warm-up while I check homework from previous night to see if there are any common
errors I should address during review
Go over Warm-up (5 minutes)
Homework from last night: (pp. 182 – 184: 3-28, 30-35, 38-40, 44) ask for any specific questions
and specifically go over #28 and # 44 (10 minutes)
#28:
a. Given
a. AB || DC
b. Alternate Interior Angles Thm
b. ∠CAB ≅∠ACD
c. ∠B ≅∠D
c. Given
d. ∠BCA ≅∠DAC
d. If 2 ∠’s ≅ then 3rd∠’s ≅ Thm
e.
AC ≅ CA
e. Reflexive Property
f.
AB ≅ CD , BC ≅ AD
f. Given
g. ΔABC ≅ ΔCDA
g. Definition of ≅ Δs
#44
a. PR || TQ
a. Given
b. ∠PRS ≅∠QTS
b. Alternate Interior Angles Thm
c. ∠RPS ≅∠TQS
c. Alternate Interior Angles Thm
d. ∠PSR ≅∠QST
d. Vertical ∠’s ≅
e. Given
e. PR ≅ QT , PS ≅ QS
f.
PQ bisects RT
f. Given
g. RS ≅ TS
g. Def of segment bisector
h. ΔPRS ≅ ΔQTS
h. Definition of ≅ Δs
Elizabeth Pawelka
Triangle Congruence (SSS and SAS)
2/24/12 p.2
Teacher Input (60 minutes)
 Activity (20 minutes)
Introduce SSS and SAS with an investigation using the Illuminations Congruence Applet:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=4 – Do examples with 3 sides (SSS), with 2 sides
and included angle (SAS), and with 2 sides and excluded angle (SSA) to show that they aren’t always
congruent. Do the first one and then have different students come up to make congruent triangles and to
try to make non-congruent triangles.
 Lecture/Examples: (40 minutes)
 In which configuration(s) were the triangles always congruent?
i. Side-Angle-Side (SAS)
ii. Side-Side-Side (SSS)
 In which configuration(s) sometimes congruent?
i. Side-Side-Angle (SSA)
 Since proofs have been problematic, include different forms of proofs (2-column/flow/paragraph)
and point out that there are only 5 types of reasons: Given, Definitions, Properties, Postulates, and
Theorems.
 Introduce the SSS Theorem: “If the three sides of one triangle are congruent to the three sides of
another triangle, then the two triangles are congruent.” Include a diagram to illustrate.
 Example 1:
 Prove: ΔABD ≅ ΔCBD
 Given: ≅ segments as marked
 Proof:
AB ≅ CB
Given
DB ≅ DB
Reflexive
AD ≅ CD
Given
ΔABD ≅ ΔCBD
by SSS
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Example 2: Prove ΔADE ≅ ΔCBE
Given: Congruent sides as marked and AC and BD bisect each other
Write on board that AE = EC and BE = ED and so
Elizabeth Pawelka

Triangle Congruence (SSS and SAS)
2/24/12 p.3
Example 3: To Prove ΔADC ≅ ΔBDC
What else do we know?
What else do we need to know?
by Reflexive Property
to prove by SSS
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Introduce SAS Postulate: “If two sides and the included angle of one triangle are congruent to two
sides and the included angle of another triangle, then the two triangles are congruent.” Include a
diagram to illustrate.
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Example 4: Prove ΔABD ≅ ΔCBD – I do one
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1. AB ≅ BC ; ∠ABD ≅∠DBC
1. Given
2. DB ≅ DB
2. Reflexive Property
3. ΔABD ≅ ΔCBD
3. SAS Postulate
Example 5: Prove ΔDFE ≅ ΔHFG – They do one
1. EF ≅ FG ; DF ≅ FH
1. Given
2. ∠DFE ≅ ∠HFG
2. Vertical ∠’s are ≅
3. ΔDFE ≅ ΔHFG
3. SAS Postulate
Example 6:
Prove: ΔAEB ≅ ΔCED
Given: The diagonal legs
are joined at their
midpoints
Since the legs are joined
at their midpoints, AE ≅
EC
and BE ≅ DE . ∠AEB ≅ ∠CED
because they are vertical ∠’s.
Therefore ΔAEB ≅ ΔCED by SAS. ■
Elizabeth Pawelka

Triangle Congruence (SSS and SAS)
2/24/12 p.4
Example 7: What is the congruency statement?
ΔCAT ≅ ΔDOG 
Closure (5 minutes)
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Today we learned to recognize congruent figures and corresponding parts
Tomorrow we’ll learn how to prove triangles congruent using the SSS and SAS Postulates
Homework (attached)
pp. 189 – 192: 1-30, 33, 41-44