+2448 1) Triangle PQR~Triangle PUT, not similar.
2) Triangle TUV~Triangle TDE, similar.
3) Triangle EDC~Triangle JKL, similar.
Are my answers correct??
+9466 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
