Note: I recommend that this page be printed out, so that the instructions are easier to follow.
In order to successfully complete a proof,
it is important to think of the definition and the construction
of a rhombus.
In the following outline, I will provide the statements, you provide the reasons.
Prove: If a quadrilateral is a rhombus, then the diagonals are perpendicular bisectors of each other.
Given: Rhombus ABCD with diagonals BD and AC intersecting at point M.
Prove: Segment AC and BD are perpendicular bisectors of each other.
First we will prove that the diagonals are bisectors of each other.
Then we will prove that the diagonals are perpendicular to each other.
10. Segment CD is congruent to segment CB.
11. Segment BM is congruent to segment MB.
12. Segment CM is congruent to segment CM.
13. Triangle CDM is congruent to triangle CBM.
14. Angle CMD is congruent to triangle BMC.
15. Angle CMD + angle BMC = 180
16. Angle CMD = 90 and angle BMC = 90
17. Angle AMB = 90
18. Angle CMD is congruent to angle DMA.
19. Angle DMA = 90
20. Segment AC is perpendicular to segment BD.
If you have any questions while trying to complete this investigation, or suggestions that would be useful, especially for use at the high school level, please send e-mail to firstname.lastname@example.org.
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