All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 What Can You Prove? (Posted on 2004-01-14)
• In the figure, above AC=BD.

• ‹ACD is a right angle.

• ‹BDC is less than 90º.

• QP and RP are perpendicular bisectors of AB and CD respectively, intersecting at P.

• AP=BP and CP=DP because all points on the perpendicular bisector of a line are equidistant from the extremities of the line.

• Triangle APC is therefore congruent to triangle BPD because of the well known "side-side-side" theorem. Now, ‹PCD=‹PDC because the base angles of an isosceles triangle are equal.

• ‹ACP=‹BDP because they are corresponding parts of congruent triangles.

• Of course, ‹ACP + ‹PCD = ‹BDP + ‹PDC because when equals are added to equals the results are equal.
Therefore, ‹ACD = ‹BDC.

But, wait, we know that this isn't true!

A mathematician had a rickety table (with top AB sitting on the floor CD with legs AC and BD) and had constructed the drawing above in an ineffectual effort to straighten the table. Can you figure out what is wrong?

 See The Solution Submitted by DJ Rating: 4.1818 (11 votes)

 Subject Author Date to SK luminita 2004-01-23 17:08:49 Why do you need Z? Dan Porter 2004-01-18 06:10:14 re: solution SilverKnight 2004-01-16 17:12:45 solution luminita 2004-01-16 16:36:09 solution Dan Porter 2004-01-15 06:53:51 No Subject Dan Porter 2004-01-15 06:53:16 re: solution Sam 2004-01-14 23:43:37 solution Charlie 2004-01-14 09:15:28

 Search: Search body:
Forums (0)