Geometry Section 4-4 1112

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Triangle Congruence -- SSS, SAS

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Geometry Section 4-4 1112

  1. 1. Section 4-4 Proving Congruence: SSS, SAS
  2. 2. 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?
  3. 3. Vocabulary 1. Included Angle: Postulate 4.1 - Side-Side-Side (SSS) Congruence: Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
  4. 4. 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:
  5. 5. 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:
  6. 6. 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 congruent
  7. 7. Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: △QUD ≅△ADU
  8. 8. Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: △QUD ≅△ADU 1. QU ≅ AD, QD ≅ AU
  9. 9. Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: △QUD ≅△ADU 1. QU ≅ AD, QD ≅ AU 1. Given
  10. 10. Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: △QUD ≅△ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU
  11. 11. 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
  12. 12. 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
  13. 13. 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
  14. 14. 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
  15. 15. 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. SSS
  16. 16. 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.
  17. 17. 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
  18. 18. 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
  19. 19. 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 V
  20. 20. 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 V W
  21. 21. 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 V W
  22. 22. 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 V W L
  23. 23. 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 V W L P
  24. 24. 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 V W L P M
  25. 25. 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 V W L P M
  26. 26. 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 V W L P M These are congruent. What possible ways could we show this?
  27. 27. Example 3 Prove the following. Prove: △FEG ≅△HIG Given: EI ≅ FH, G is the midpoint of EI and FH
  28. 28. Example 3 Prove 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
  29. 29. Example 3 Prove 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
  30. 30. Example 3 Prove 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.
  31. 31. Example 3 Prove 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. Midpoint Thm.
  32. 32. Example 3 Prove 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. Midpoint Thm. ∠FGE ≅ ∠HGI3.
  33. 33. Example 3 Prove 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. Midpoint Thm. ∠FGE ≅ ∠HGI3. 3. Vertical Angles Thm.
  34. 34. Example 3 Prove 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. Midpoint Thm. ∠FGE ≅ ∠HGI3. 3. Vertical Angles Thm. 4. △FEG ≅△HIG
  35. 35. Example 3 Prove 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. Midpoint Thm. ∠FGE ≅ ∠HGI3. 3. Vertical Angles Thm. 4. △FEG ≅△HIG 4. SAS
  36. 36. Problem Set
  37. 37. Problem Set p. 266 #1-19 odd, 31, 39, 41 "Doubt whom you will, but never yourself." - Christine Bovee

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