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RainbowPanda  Feb 19, 2018
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#1
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1) Triangle PQR~Triangle PUT, not similar.

2) Triangle TUV~Triangle TDE, similar.

3) Triangle EDC~Triangle JKL, similar.

RainbowPanda  Feb 19, 2018
edited by RainbowPanda  Feb 19, 2018
#2
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1)  " Triangle PQR~Triangle PUT, not similar. "

This says, "triangle PQR is similar to triangle PUT, not similar."

If they are not similar then we can't make a similarity statement!

But these triangles actually are similar...

∠PQR  ≅  ∠PUT   because they both are marked by a red line, and

∠QPR  ≅  ∠UPT   because they are vertical angles.

Since two of the angles are the same, the triangles are similar.

△PQR ~ △PUT

2)

∠VTU  ≅  ∠DTE  because they are vertical angles.

If these triangles are similar, then this must be true of the sides adjacent to the angle we know is shared by both triangles:

$$\frac{\text{shorter side of first triangle}}{\text{shorter side of second triangle}}\,=\,\frac{\text{longer side of first triangle}}{\text{longer side of second triangle}} \\~\\ \frac{19}{63}\,=\,\frac{27}{98}$$

Since this is not true, the triangles are not similar.

3)

If the triangles are similar, then this must be true:

$$\frac{32}{56}\,=\,\frac{40}{70}\,=\,\frac{48}{84} \\~\\ \frac47\,=\,\frac47\,=\,\frac47$$

Since this is true, the triangles are similar.

△EDC ~ △JKL

hectictar  Feb 19, 2018

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