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Given: Trapezoid MINS with median TR Prove: TR || IN , TR || MS R. TR = ( MS+ IN) Proof: Statements Reasons 1. Trapezoid MINS with median TR Draw IS, with P as its midpoint. 1. Given 2. 2. P =-MS and TP || MS 3. 3. 4. 4. Theorem 5 (Midline theorem), on AINS 5. MS || IN 6. TP || IN 7. TP and PR are both parallel to TP || IN. Thus, T, P, and R are collinear. 5. 6. 7. 8. TR TP+ PR 8. 9. 9. Substitution 10. TR = 10.

Given: Trapezoid MINS with median TR Prove: TR || IN , TR || MS R. TR = ( MS+ IN) Proof: Statements Reasons 1. Trapezoid MINS with median TR Draw IS, with P as its midpoint. 1. Given 2. 2. P =-MS and TP || MS 3. 3. 4. 4. Theorem 5 (Midline theorem), on AINS 5. MS || IN 6. TP || IN 7. TP and PR are both parallel to TP || IN. Thus, T, P, and R are collinear. 5. 6. 7. 8. TR TP+ PR 8. 9. 9. Substitution 10. TR = 10.

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.
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 19E: Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of...
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Given: Trapezoid MINS with median TR Prove: TR || IN, TR || MS T R. (MS + IN) TR = Proof: Statements Reasons 1. Given 1. Trapezoid MINS with median TR Draw IS, with P as its midpoint. 2. 2. TP = 3. -MS and TP | MS 3. 4. 4. Theorem 5 (Midline theorem), on AINS 5. MS || IN 5. 6. TP || IN 7. TP and PR are both parallel to TP || IN. Thus, T, P, and R are collinear. 6. 7. 8. TR = TP+ PR 8. 9. 9. Substitution M + IN) 10. TR = 10.
Transcribed Image Text:Given: Trapezoid MINS with median TR Prove: TR || IN, TR || MS T R. (MS + IN) TR = Proof: Statements Reasons 1. Given 1. Trapezoid MINS with median TR Draw IS, with P as its midpoint. 2. 2. TP = 3. -MS and TP | MS 3. 4. 4. Theorem 5 (Midline theorem), on AINS 5. MS || IN 5. 6. TP || IN 7. TP and PR are both parallel to TP || IN. Thus, T, P, and R are collinear. 6. 7. 8. TR = TP+ PR 8. 9. 9. Substitution M + IN) 10. TR = 10.
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