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 No trigonometry, no algebra (Posted on 2005-12-23)
Look at the drawing below, where AB = BC = CD = DT = h, and TD perpendicular to AD:
```
o T
|
| (h)
|
|
+----------+----------+----------o
A    (h)   B    (h)   C    (h)   D```
The line AT makes an angle x with AD; the line BT makes an angle y with BD; the line CT makes an angle z with CD.

Using only geometry, prove that (angle x) + (angle y) = (angle z).

 See The Solution Submitted by pcbouhid Rating: 3.0000 (1 votes)

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 Solution | Comment 6 of 10 |
` `
`   |CT|     h*sqrt(2)         h         |CB|  ------ = ----------- = ----------- = ------   |CA|        2*h        h*sqrt(2)     |CT|`
`Therefore, triangles ACT and TCB are similar.`
`Therefore, angles CAT and CTB are equal.`
`Angle z is an exterior angle of triangle CBT.`
`Therefore, angle(z) = angle(CBT) + angle(CTB)`
`                    = angle(CBT) + angle(CAT)`
`                    = angle(y) + angle(x)`
` `

 Posted by Bractals on 2005-12-24 04:35:23

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