Intercept theorem in triangles
Its straight line geometry time and I've reached another point that I cannot seem to get my head round (though I am sure it will be something obvious).
Triangles PQR and XYZ are such that:
1. Angle P = Angle X
2. Angle Q = Angle Z
3. XY = 3cm
4. YZ = 4cm
5. PQ = 7cm
6. PR = 12cm
I need to find the lengths of XZ and QR.
My answer so far
So I have a large PQR triangle drawn on my page with a line ZY which is parallel to QR, the symbols for angles are put in there to indicate that the two triangles are similar and that PQR is an enlargement of XYZ.
So to find XZ I knew the ratios of the intercepts would be the same so:
PZ:QR = PY:PR
so PZ:7 = 3:12 (or 1:4)
so PZ = (7*3)/12 (or 7/4)
How do I go about working out QR?