geometry section 4-4 1112
DESCRIPTION
Triangle Congruence -- SSS, SASTRANSCRIPT
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Section 4-4
Proving Congruence: SSS, SAS
Monday, February 6, 2012
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Essential Questions
How do you use the SSS Postulate to test for triangle congruence?
How do you use the SAS Postulate to test for triangle congruence?
Monday, February 6, 2012
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Vocabulary1. Included Angle:
Postulate 4.1 - Side-Side-Side (SSS) Congruence:
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
Monday, February 6, 2012
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Vocabulary1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence:
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
Monday, February 6, 2012
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Vocabulary1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three corresponding sides of a second, then the triangles are congruent
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
Monday, February 6, 2012
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Vocabulary1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three corresponding sides of a second, then the triangles are congruent
Postulate 4.2 - Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are congruent to two corresponding sides and included angle of a second triangle, then the triangles are congruent
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU 2. Reflexive
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU 2. Reflexive
3. DU ≅ UD
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU 2. Reflexive
3. DU ≅ UD 3. Symmetric
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU 2. Reflexive
3. DU ≅ UD 3. Symmetric
4. QUD ≅ADU
Monday, February 6, 2012
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Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
2. DU ≅ DU 2. Reflexive
3. DU ≅ UD 3. Symmetric
4. QUD ≅ADU 4. SSS
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
yMonday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
D
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
W
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
W
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
WL
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
WL
P
Monday, February 6, 2012
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Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
WL
P
M
Monday, February 6, 2012
![Page 25: Geometry Section 4-4 1112](https://reader034.vdocument.in/reader034/viewer/2022051412/54b2ba304a7959a15d8b45c3/html5/thumbnails/25.jpg)
Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
WL
P
M
Monday, February 6, 2012
![Page 26: Geometry Section 4-4 1112](https://reader034.vdocument.in/reader034/viewer/2022051412/54b2ba304a7959a15d8b45c3/html5/thumbnails/26.jpg)
Example 2∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM
has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not, providing a logical argument for your statement.
x
y
DV
WL
P
M
These are congruent. What possible ways could we show this?
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2.
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2. 2. Def. of midpoint
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2. 2. Def. of midpoint
∠FGE ≅ ∠HGI3.
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2. 2. Def. of midpoint
∠FGE ≅ ∠HGI3. 3. Vertical Angles
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2. 2. Def. of midpoint
∠FGE ≅ ∠HGI3. 3. Vertical Angles
4. FEG ≅HIG
Monday, February 6, 2012
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Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
1. EI ≅ FH , G is the midpoint of EI and FH 1. Given
FG ≅ HG, EG ≅ IG2. 2. Def. of midpoint
∠FGE ≅ ∠HGI3. 3. Vertical Angles
4. FEG ≅HIG 4. SAS
Monday, February 6, 2012
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Check Your Understanding
Review p. 266 #1-4
Monday, February 6, 2012
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Problem Set
Monday, February 6, 2012
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Problem Set
p. 267 #5-19 odd, 31, 39, 41
"Doubt whom you will, but never yourself." - Christine Bovee
Monday, February 6, 2012