Download GEOMETRY LP-W10-Q2-011712 4_4 and 4_5 Tuesday

LP-W10-Q2-01/17/2012
What’s man’s first duty?
The answer’s brief: to be himself
Henrik Ibsen, 1828-1906
Norwegian writer, dramatist, poet.
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GEOMETRY 01/17/2012
www.miamiseniorhs.com
LESSON PLAN RESOURCES.xlsx2
MA.912.A.3.1 MA.912.A.3.9 MA.912.A.3.12 MA.912.G.1.1
MA.912.G.1.3 MA.912.G.1.4 MA.912.G.4.1 MA.912.G.4.2
MA.912.G.8.4 MA.912.G.8.6
Chapter 4:
Proving Triangle Congruency
Sections:
4.4 Are there Congruence Shortcuts?
4.5 Are There Other Congruence Shortcuts?
Objectives:
-Apply postulates and theorems to prove triangle congruency.
SAS, ASA, AAS, SSS
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ASSIGNMENTS: 4.4 and 4.5
1. Proving Congruency. Examples.
2. Interactive practice. (KA)
3. DG Workbook Pgs. 26, 27 and 28
4. Homework: DG Pgs. 24 and 25
SSS Postulate.
If three sides of one triangle are equal to the corresponding
parts of another triangle, the triangles are congruent.
1. Discussion of conjectures, definitions and examples.
1. Given: X is the midpoint of ̅̅̅̅
𝑨𝑩 and ̅̅̅̅
𝑪𝑫.
AC = BD
Prove:
AXC ≅
BXD
A
(IA)
C
X
D
B
2
STATEMENTS
1. CX = DX
2. AX = BX
3. AC = BD
4. AXC ≅ BXD
REASONS
GIVEN
GIVEN
GIVEN
SSS POSTULATE
̅̅̅̅
2. Given: S is the midpoint of 𝑻𝑽
TR = VR
Prove: TSR ≅ VSR
T
STATEMENTS
1. TS = VS
2. RS = RS
3. TR = VR
4. TSR ≅ VSR
(IA)
R
S
V
REASONS
GIVEN
REFLEXIVE PROPERTY
GIVEN
SSS POSTULATE
3
NOW TRY # 3g
3. Given: ZY = WX
ZW = YZ
Prove: TRS ≅
Z
Y
VSR
W
STATEMENTS
1. ZY = WX; ZW = YX
2. WY = WY
3. WZY ≅ YXW
X
REASONS
GIVEN
REFLEXIVE PROPERTY
SSS POSTULATE
4. Suppose you wish to use the SSS Postulate to prove that
DEF ≅ JKM. What value must x have? (IA)
Reasoning: To prove triangle congruency using SSS Postulate,
we must be aware of that all corresponding sides of the
triangles are congruent. Thus, FD = MJ, DE = JK and
FE = MK. Since FD = MJ we can stay the equation 2x = 8.
Solving this equation we get x=4
4
F
M
2X
8
D
E
12
J
Now, find the x value, if
triangles.
13
DEF and
F
K
KJM are congruent
M
X+7
16
E
K
D
10
13
J
5. Given:
ABC and RST, with AB = RS, BC = ST, and
AC = RT. Copy and complete each row of angle measures.
(IA)
<A
70°
100°
<B
80°
<C
<R
<S
<T
20°
52°
63°
x°
y°
SAS Postulate
5
If two sides and the included angle of one triangle are equal
to the corresponding parts of another triangle, the triangles
are congruent.
6. Given: ⃗⃗⃗⃗⃗⃗⃗
𝒁𝑾 bisects <XZY
XZ = YZ
Prove:
XWZ ≅ YWZ
Z
X
4.
W
STATEMENTS
1. <XZW = < WZY
2. ZW = ZW
3. XZ = YZ
XWZ ≅ YWZ
Y
REASONS
1. Given: ⃗⃗⃗⃗⃗⃗⃗
𝒁𝑾 bisects <XZY
2. Reflexive Property
3. Given
4. SAS Postulate
Try
7. Complete the proof by supplying the reasons.
A
D
6
C
X
B
Given: X is the midpoint of ̅̅̅̅
𝑨𝑩 and ̅̅̅̅
𝑪𝑫
Prove:
4.
AXC ≅
BXD
STATEMENTS
1. CX = DX AX=BX
2. AX=BX
3. <AXC = <BXD
AXC ≅ BXD
REASONS
ASA Postulate
If two angles and the included side of one triangle are
equal to the corresponding parts of another triangle, the
triangles are congruent.
7
Name the side included between the two angles.
X
C 5
R
K
8 B
6
9
A 4
1. <R and <K
2. <X and <R
7
3. <5 and <6
<7 and <8
D
8. Given: M is the midpoint of ̅̅̅̅
𝒀𝒁.
⃗⃗⃗⃗⃗⃗⃗
𝑴𝒀 bisects <OMV
Prove:
YOM ≅
ZUM
O
Y
U
1 M 2
Z
3
V
8
STATEMENTS
1. <1= <3
2. <2 = <3
3. <1 = <2
4. YM = ZM
5. < Y = < Z
6. YOM ≅
ZUM
REASONS
1. Given: ⃗⃗⃗⃗⃗⃗⃗
𝑴𝒀 bisects
<OMV
2. Vertical angles are
congruent
3. Substitution Postulate
4. Given: M is the midpoint
of⃗⃗⃗⃗⃗⃗
𝒀𝒁
5. Given
6. ASA Postulate.
AAS Theorem
If two angles and a non-included side of one triangle are equal
to the corresponding parts of another triangle, the triangles
are congruent.
HL Theorem
If the hypotenuse and a leg of one right triangle are equal to
the corresponding parts of another right triangle, the triangles
are congruent.
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9. Given: <B and <X are right angles.
BY = AX
Prove: ABY ≅ YXA
X
A
STATEMENTS
1. <B and <X are right angles
2. AY = AY
3. BY = AX
4. ABY ≅
YXA
Y
B
REASONS
1. Given
2. Reflexive Property
3. Given
4. HL
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STRATEGIES AND PRACTICES
PROVIDE HINTS AND FEEDBACK
INTERACTIV E PARTICIPATION
HAVING STUDENTS TEACH WHAT THEY LEARNED TO SOMEONE ELSE
BLOOM TAXONOMY (CONGNITIVE DOMAIN)
1. KNOWLEDGE
Name
2. COMPREHENSION
Recognize
3. APPLICATION
Sketch
4. ANALYSIS
Dif ferentiate
TEACHING RESOURCES & MATERIALS
DOCUMENT CAMERA
WHITE BOARD
MARKERS
COMPASS
PROTRACTOR
CARDBOARD
PAPER
RULER
11
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