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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 63E
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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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