Question

Given: Line HR is parallel to line GM
Prove: PR/OM = PH/OG
diagram: http://slimber.com/gallery/image/triangle:g289977.html

Answer 1

Statements | Reasons
-------------------------------------------------------------------------
1. Line HR || line GM | 1. Given
2. <JRH is congr to <JMO | 2. Corresp <s || lines
3. <JHR is congr to <JGO | 3. Same as 2
4. triangle JRH ~ triangle JMG | 4. AA similarity
5. PR/OM = JP/PO |5. Similar triangles have proportional parts
6. JP/PO = PH/OG | 6. Same as 5.
7. PR/OM = PH/OG | 7. Substitution (or transitive prop of equality)

Answer 2

Part of that is wrong. it should be triangle JPR ~ triangle JMO for statement#4

Answer 3

Statements | Reasons
-----------------------------------------------------------------
1. Line HR || line GM | 1. Given
2. <JRH is congr to <JMO | 2. Corresp <s || lines are congruent
3. <JPR is congr to <JOM | 3. Corresp <s || lines are congruent
4. Triangle JPR ~ triangle JOM | 4. AA similarity
5. PR/OM = JP/JO | 5. Similar triangles have proportional parts
6. <JHR is congr to <JGO | 6. Corresp <s || lines are congruent
7. <JPH is congr to <JOG | 7. Corresp <s || lines are congruent
8. triangle JHP ~ triangle JGO | 8. AA similarity
9. JP/JO = PH/OG | 9. Similar triangles have proportional parts
10. PR/OM = PH/OG | 10. Substitution (or transitive prop of equality)

Answer 4

@personperson99 Thanks for pointing that out. I went over the whole proof and corrected it. I think did it on paper and tried a few times until I got it right, but I copied it incorrectly. I just did it again, and this version is correct.