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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2007-05-19 21:56:08

Identity
Member
Registered: 2007-04-18
Posts: 934

Another prooof

faint Congruency and Similar triangles test tomorrow, most of it seems all right, but stuff like THIS is really confusing! Help plz.

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#2 2007-05-19 22:29:43

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Another prooof

ABCD and ARQP are squares, right? (This isn’t stated but from the diagram (if drawn to scale) they look like squares – so I presume this is the case.)

Then I can see that rotating ΔBAR through 90° clockwise will fit it into ΔDAP. Hence the two triangles are congruent (and DÂP = BÂR).

PS: Actually, if you want a more analytical proof, that’s quite straightforward too …

DÂP + PÂB = 90°
BÂR + PÂB = 90°
∴ DÂP = BÂR

Last edited by JaneFairfax (2007-05-19 22:33:37)

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#3 2007-05-19 22:31:25

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Another prooof

Yeah sorry I forgot to mention that. They are both squares

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