Q1. If $\Delta ABC \sim \Delta DEF$ such that $\text{ar}(\Delta ABC) = 64\text{ cm}^2$ and $\text{ar}(\Delta DEF) = 121\text{ cm}^2$. If $EF = 15.4\text{ cm}$, then $BC$ is:
Q2. In $\Delta ABC$, $DE \parallel BC$. If $\frac{AD}{DB} = \frac{2}{3}$ and $AC = 18\text{ cm}$, then $AE$ is:
Q3. If $\Delta ABC \sim \Delta QRP$, $\frac{\text{ar}(\Delta ABC)}{\text{ar}(\Delta QRP)} = \frac{9}{4}$, and $BC = 15\text{ cm}$, then $RP$ is:
Q4. Assertion (A): If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Reason (R): If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
Q5. A vertical stick 20 cm long casts a shadow 16 cm long on the ground. At the same time, a tower casts a shadow 48 m long on the ground. Find the height of the tower.
Solve on white paper.
Q6. In the given figure, $\Delta ABE \cong \Delta ACD$. Prove that $\Delta ADE \sim \Delta ABC$.
Q7. $E$ is a point on the side $AD$ produced of a parallelogram $ABCD$ and $BE$ intersects $CD$ at $F$. Show that $\Delta ABE \sim \Delta CFB$.
Q8. In $\Delta ABC$, $D$ is a point on side $BC$ such that $\angle ADC = \angle BAC$. Prove that $CA^2 = CB \times CD$.
Q9. 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.
Q10. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Q11. Case Study: Mirror Reflection
A girl of height 1.5 m wants to know the height of a tree. She places a mirror on the ground at a distance of 1.5 m from her feet and 12 m from the base of the tree. Looking into the mirror, she sees the top of the tree.
(i) Which criterion of similarity is used here?
(ii) Find the height of the tree.
(iii) If she moves the mirror so that it is at a distance of 8 m from the tree, at what distance from the mirror should she stand to see the top of the tree?