Q1. If $\Delta ABC \sim \Delta DEF$, $AB = 4$ cm, $DE = 6$ cm, $EF = 9$ cm and $FD = 12$ cm, then the perimeter of $\Delta ABC$ is:
Q2. In $\Delta ABC$, $DE \parallel BC$ such that $AD = x$, $DB = x-2$, $AE = x+2$ and $EC = x-1$. The value of $x$ is:
Q3. The areas of two similar triangles are in the ratio 4:9. The ratio of their corresponding medians is:
Q4. Assertion (A): All congruent triangles are similar. Reason (R): All similar triangles are congruent.
Q5. In the given figure, $DE \parallel BC$. If $AD = 1.5$ cm, $DB = 3$ cm and $AE = 1$ cm, find $EC$.
Solve on white paper.
Q6. The diagonals of a trapezium ABCD with $AB \parallel DC$ intersect each other at the point O. If $AB = 2CD$, find the ratio of the areas of triangles AOB and COD.
Q7. $\Delta ABC \sim \Delta PQR$. The perimeter of $\Delta ABC$ is 32 cm and the perimeter of $\Delta PQR$ is 48 cm. If $PR = 6$ cm, find the length of $AC$.
Q8. In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $\angle 1 = \angle 2$. Show that $\Delta PQS \sim \Delta TQR$.
Q9. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Q10. State and prove the Basic Proportionality Theorem (Thales Theorem).
Q11. Case Study: Scale Models
A scale drawing of an object is the same shape as the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents.
(i) If a model of a building is made on a scale of 1:50, and the height of the model is 20 cm, find the actual height of the building.
(ii) If the actual length of a room is 10 m and in the drawing it is 5 cm, what is the scale used?
(iii) Two similar triangles have a scale factor of 3:5. If the area of the smaller triangle is 81 sq cm, find the area of the larger triangle.