Question

10. In the adjoining figure, if
angleXZY = 2 angleYXZ then, find angle ZXP.​

Answer 1

Answer:

AAA postulate for symmetry :

If all three corresponding interior angles of 2 triangles are the same, then the two triangles are similar.

In general, if two corresponding angles are equal, then the remaining angle will also be equal, as they always add up to 180

o

.

In figure (i), if ∠A=∠D,∠B=∠E,∠C=∠F by AAA postulate we can say that 2 triangles are similar.

In fig (2) given ∠YXZ=∠XPZ

We can divide the given figure (iii) into two separate triangles.

Consider △XYZ and △PXZ.

∠YXZ=∠XPZ ....(given)

∠XZY=∠XZP ...(∵ they are same )

∠XYZ=∠PXZ ...(∵ sum of angles = 180°)

Hence, by AAA postulate,

△XYZ∼△PXZ

∴

ZY

ZX

=

XZ

PZ

....cpst