Section 4-4 Proving Congruence: SSS, SAS Monday, February 6, 2012
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Section 4-4
Proving Congruence: SSS, SAS
Monday, February 6, 2012
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
Vocabulary1. Included Angle:
Postulate 4.1 - Side-Side-Side (SSS) Congruence:
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
Monday, February 6, 2012
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
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
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
Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
Monday, February 6, 2012
Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU
Monday, February 6, 2012
Example 1Prove the following.
Given: QU ≅ AD, QD ≅ AU
Prove: QUD ≅ADU
1. QU ≅ AD, QD ≅ AU 1. Given
Monday, February 6, 2012
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Example 3Prove the following.
Prove: FEG ≅HIG
Given: EI ≅ FH, G is the midpoint of EI and FH
Monday, February 6, 2012
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
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
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
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
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
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
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
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
Check Your Understanding
Review p. 266 #1-4
Monday, February 6, 2012
Problem Set
Monday, February 6, 2012
Problem Set
p. 267 #5-19 odd, 31, 39, 41
"Doubt whom you will, but never yourself." - Christine Bovee
Monday, February 6, 2012
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