Q. Fill in the blanks using the correct word given in brackets :
(i) All circles are _______. (congruent, similar)
(ii) All squares are ________. (similar, congruent)
(iii) All _______ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are _______ and (b) their corresponding sides are ______. (equal, proportional)

Q. Give two different examples of pair of:
(i) similar figures. (ii) non-similar figures.

Q. State whether the above quadrilaterals are similar or not:

Q. Using Theorem $6.1,$ prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Q. The diagonals of a quadrilateral $ABCD$ intersect each other at the point $O$ such that $\frac{AO}{BO}=\frac{CO}{DO}$. Show that $ABCD$ is a trapezium.

Q. In Fig., $DE||AC$ and $DF||AE$. Prove that $\frac{BF}{FE}=\frac{BE}{EC}$.

Q. In Fig., (i) and (ii), $DE||BC$. Find $EC$ in (i) and $AD$ in (ii).

Q. In Fig., if $LM||CB$ and $LN||CD$, prove that $\frac{AM}{AB}=\frac{AN}{AD}$.

Q. In given figure, $A,B$ and $C$ are points on $OP,OQ$ and $OR$ respectively such that $AB||PQ$ and $AC||PR$. Show that $BC||QR$.

Q. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Q. $ABCD$ is a trapezium in which $AB||DC$ and its diagonals intersect each other at the point $O.$ Show that $\frac{AO}{BO}=\frac{CO}{DO}$.

Q. In Fig., $DE||OQ$ and $DF||OR$. Show that $EF||QR$.

Q. $E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $△PQR$. For each of the following cases, state whether $EF||QR$ :
(i) $PE=3.9$ cm, $EQ=3$ cm, $PF=3.6$ cm and $FR=2.4$ cm
(ii) $PE=4$ cm, $QE=4.5$ cm, $PF=8$ cm and $RF=9$ cm
(iii) $PQ=1.28$ cm, $PR=2.56$ cm, $PE=0.18$ cm and $PF=0.36$ cm

Q. $S$ and $T$ are points on sides $PR$ and $QR$ of $△PQR$ such that $\angle P=\angle RTS$. Show that $△RPQ\sim △RTS$.

Q. In Fig, $△ODC\sim △OBA,\angle BOC={125}^o$ and $\angle CDO={70}^o$. Find $\angle DOC,\angle DCO$ and $\angle OAB$.

Q. State which pairs of triangles in Fig. are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :

Q. In Fig, altitudes $AD$ and $CE$ of $△ABC$ intersect each other at the point $P.$ Show that:
(i) $△AEP\sim △CDP$
(ii) $△ABD\sim △CBE$
(iii) $△AEP\sim △ADB$
(iv) $△PDC\sim △BEC$

Q. In the given figure., if $△ABE\cong △ACD$, show that $△ADE\sim △ABC.$

Q. Diagonals $AC$ and $BD$ of a trapezium $ABCD$ with $AB||DC$ intersect each other at the point $O.$ Using a similarity criterion for two triangles, show that $\frac{OA}{OC}=\frac{OB}{OD}$.

Q. In Fig., $\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1=\angle 2$. Show that $△PQS\sim △TQR$.