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Section 3.7 Angle-Side Theorems. By: Kellan Hirschler and Katherine Rosencrance. Theorem 20: If two sides of a triangle are congruent, the angles opposite the sides are congruent. Symbolic form: If , then (If sides, then angles). E. Given:. Conclusion:. A. T.

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## Section 3.7 Angle-Side Theorems

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**Section 3.7 Angle-Side Theorems**By: Kellan Hirschler and Katherine Rosencrance**Theorem 20: If two sides of a triangle are congruent, the**angles opposite the sides are congruent. Symbolic form: If , then (If sides, then angles) E Given: Conclusion: A T**Theorem 21: If two angles of a triangle are congruent, the**sides opposite the angles are congruent. Symbolic form: If , then (If angles, then sides) P Given: I E Conclusion: E I**S**R 1. 1. Given I G 2. Given 2. 3. 3. If angles, then sides 4. PIK PGK 4. SAS (1,2,3) P Prove: PIK PGK I G K**Theorem: If two sides of a triangle are not congruent, then**the angles opposite them are not congruent and the larger angle is opposite the longer side. Symbolic Form: If , then . Longer Shorter Larger Smaller**Theorem: If two angles of a triangle are not congruent, then**the sides opposite them are not congruent, and the longer side is opposite the larger angle. Symbolic Form: If , then . Longer Shorter Larger Smaller**2 ways to prove a triangle is isosceles:**If , then is isosceles. If , then is isosceles. Equilateral triangle <=> Equiangular triangle <=>**H**S R 1. OHR EHS 1. Given 2. 2. Given 3. If sides, then angles 3. OH O R S E 4. ASA (1,2,3) 4. OHR EHS OHR EHS 5. Given: 5. CPCTC Prove:**REVIEW**O Given: Conclusion: W L W L R Given: O W Conclusion: O W**S**R K A T I 1. 1. Given ; KEI is isos. with 2. If the triangle is isos., then the legs are congruent and 2. E 3. If the triangle is isos., then the base angles are congruent. K Given: 3. I 4. KET IEA KEI is isos. with and Prove: KET IEA 4. SAS (1,2,3)**M**S R ; 1. 1. Given A S ; A is the mp. of ; S is the mp. of 2. R 2. If sides, then angles. T R K E T 3. ; 3. Mp. divides segments into 2 congruent segments. Given: 4. 4. Same as 3. A is the mp of TSE 5. RAK 5. SAS ( 4, 2, 1) S is the mp of 6. 6. CPCTC Prove:**Works Cited**Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry: For Enjoyment and Challenge. Evanston, Illinois: McDougal Littell, 1991. Print.

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