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separate sheet of paper. Given: S is the midpoint of AP Ris the midpoint of Al Prove: SRFI SR =;PI

separate sheet of paper. Given: S is the midpoint of AP Ris the midpoint of Al Prove: SRFI SR =;PI

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Activity: Prove the midine theorem by following the given example above. Write your answer on a separate sheet of paper. Given: S is the midpoint of AP R is the midpoint of Al Prove: SR|PI SR =PI %3D
Transcribed Image Text:Activity: Prove the midine theorem by following the given example above. Write your answer on a separate sheet of paper. Given: S is the midpoint of AP R is the midpoint of Al Prove: SR|PI SR =PI %3D
The segment that joins the midpoints of two Given: I is the midpoint of AK sides of a triangle is Mis the midpoint of KV parallel to the third side Prove: IM||AV and half as long. IM = AV A Statements 1. I is the midpoint of AK Statements 9. Al = VY Reasons Transitive Property of Segment Congruence Statements 7 and 9 Reasons Given M is the midpoint of KV 10. Quadrilateral IAVY is a 2. Extend IM and locate Construction (Definition of parallelogram point Y such that IM = parallelogram |- equal opposite sides are MY 3. KM = MV Definition of Midpoint Vertical Angles parallel) 4. ZKMI = ZVMY 11. IY||AV Definition of Parallelogram Theorem 5. ΔΚΜΙΞΔΜ SAS Congruence 12. IY = IM + MY 13. IM + MY = 21M Postulate Corresponding Parts of Congruent Triangles are Congruent Definition of Betweenness Statements 2 and 12, and Substitution Opposite sides of %3D 6. KI = VY ZIKM = LYVM 14. AV = IY parallelogram are (СРСТC) Converse of the congruent Statements 12 and 14, and 7. TA||VY 15. 2IM = AV Alternative Interior Angles Theorem Definition of Midpoint Substitution Multiplication Property of Equality 16. IM =AV 8. KI = AI Activity: Prove the midline theorem by following the given example above. Write your answer on a separate sheet of paper. Given: S is the midpoint of AP Ris the midpoint of AI Prove: SR||PI SR =PI %3!
Transcribed Image Text:The segment that joins the midpoints of two Given: I is the midpoint of AK sides of a triangle is Mis the midpoint of KV parallel to the third side Prove: IM||AV and half as long. IM = AV A Statements 1. I is the midpoint of AK Statements 9. Al = VY Reasons Transitive Property of Segment Congruence Statements 7 and 9 Reasons Given M is the midpoint of KV 10. Quadrilateral IAVY is a 2. Extend IM and locate Construction (Definition of parallelogram point Y such that IM = parallelogram |- equal opposite sides are MY 3. KM = MV Definition of Midpoint Vertical Angles parallel) 4. ZKMI = ZVMY 11. IY||AV Definition of Parallelogram Theorem 5. ΔΚΜΙΞΔΜ SAS Congruence 12. IY = IM + MY 13. IM + MY = 21M Postulate Corresponding Parts of Congruent Triangles are Congruent Definition of Betweenness Statements 2 and 12, and Substitution Opposite sides of %3D 6. KI = VY ZIKM = LYVM 14. AV = IY parallelogram are (СРСТC) Converse of the congruent Statements 12 and 14, and 7. TA||VY 15. 2IM = AV Alternative Interior Angles Theorem Definition of Midpoint Substitution Multiplication Property of Equality 16. IM =AV 8. KI = AI Activity: Prove the midline theorem by following the given example above. Write your answer on a separate sheet of paper. Given: S is the midpoint of AP Ris the midpoint of AI Prove: SR||PI SR =PI %3!
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