Questions on Similaity Based on the Properties of Transversals

Q. When two parallel lines are transected by the two intersecting lines then the two triangles so formed are

1. Congruent to each other
2. Similar to each other
3. Right angled triangles
4. None

Q. In $△ABC,P$ divides $AB$ in the ratio $3:5$, and $PQ\parallel BC.$ The length of $PQ$ (in inches) is (All lengths are in inches)

Q. Given $△ABC$, find the values of $p$ and $q$

1. 4 cm, 5 cm
2. 6 cm , 5 cm
3. 7 cm , 6 cm
4. 7.2 cm, 6.4 cm

Q. In the given figure,

$XY||QR$, $XZ||PR$ and $YZ||PQ$.
Which of the following correct?

1. $△XYZ\sim △RQP$
2. $△XYZ\sim △PQR$
3. $\angle X=\angle P$
4. $\angle Y=\angle R$

Q. In the given figure, $AB||FH$, $DF||BG$, the which of the following is correct?

1. $△ADE~△HGC$
2. $△ABC~△HFE$
3. $AE.FE=DE.EH$
4. $AB.HF=BC.FE$