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# Geometry Section 4-4 1112

## on Feb 06, 2012

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Triangle Congruence -- SSS, SAS

Triangle Congruence -- SSS, SAS

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## Geometry Section 4-4 1112Presentation Transcript

• Section 4-4 Proving Congruence: SSS, SASMonday, 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
• Vocabulary 1. Included Angle: Postulate 4.1 - Side-Side-Side (SSS) Congruence: Postulate 4.2 - Side-Angle-Side (SAS) Congruence:Monday, February 6, 2012
• Vocabulary 1. 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
• Vocabulary 1. 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
• Vocabulary 1. 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 congruentMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADUMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AUMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. GivenMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DUMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. ReﬂexiveMonday, February 6, 2012
• Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. Reﬂexive 3. DU ≅ UDMonday, February 6, 2012
• Example 1 Prove 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. SymmetricMonday, February 6, 2012
• Example 1 Prove 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 ≅ADUMonday, February 6, 2012
• Example 1 Prove 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. SSSMonday, 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. D 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. D x V 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. D x V W 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. D x V W 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. D x V W L 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. D P x V W L 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. D P x V W L M 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. D P x V W L M 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. D P x V W These are congruent. What L possible ways could we show this? M yMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIGMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FHMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. GivenMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IGMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpointMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGIMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical AnglesMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical Angles 4. FEG ≅HIGMonday, February 6, 2012
• Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical Angles 4. FEG ≅HIG 4. SASMonday, February 6, 2012
• Check Your Understanding Review p. 266 #1-4Monday, February 6, 2012
• Problem SetMonday, February 6, 2012
• Problem Set p. 267 #5-19 odd, 31, 39, 41 "Doubt whom you will, but never yourself." - Christine BoveeMonday, February 6, 2012