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July 18th, 2017, 08:24 AM   #1
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Similar triangles with scale factor sqrt 3

Hi!

You have triangle ABC. On BC there's a point, D. AD splits ABC into two similar triangles (uniform triangles?) hence ABD~ACD. The scale factor is sqrt 3; what are the sizes of the angles in ABC?

Last edited by skipjack; July 18th, 2017 at 09:59 AM.
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July 18th, 2017, 10:30 AM   #2
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If $\small\triangle$ABD ~ $\small\triangle$CAD, they want you to find 30$^\circ\!$, 60$^\circ\!$ and 90$^\circ\!$.
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July 19th, 2017, 02:57 AM   #3
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How?

Okey! But how do I find those angles?
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July 19th, 2017, 03:10 AM   #4
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Angles BDA and ADC are equal, so they are both 90$^\circ\!$. Hence angle BAC is also 90$^\circ\!$.

Can you make progress from there?
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July 19th, 2017, 12:17 PM   #5
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But who says that BD=DC? Bc if angles BDA and ADC are equal, the scale factor will be 1, right? As AD will be the same side in both triangles.
And further on, if BDA and ADC are equal, it will split BC in two equal parts, hence scale factor 1 again.
Or?
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July 19th, 2017, 11:59 PM   #6
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I didn't assert that BD = DC. One is 3 times the other.
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