Free printable worksheet
Class 9 · Mathematics · 10 Aug 2026
Which congruence criterion is NOT sufficient to prove that two triangles are congruent?
[1 mark]The areas of two similar triangles are 81 cm² and 49 cm² respectively. If the altitude of the first triangle is 6.3 cm, find the corresponding altitude of the second triangle.
[2 marks]Let \Delta ABC \sim \Delta PQR. If \frac{\text{Perimeter}(\Delta ABC)}{\text{Perimeter}(\Delta PQR)} = \frac{3}{5} and QR = 15 cm, what is the length of BC?
[2 marks]Match each type of triangle with its defining property regarding sides.
[2 marks]| Column A | Column B |
|---|---|
| 1. Scalene triangle | a. All three sides are of different lengths |
| 2. Isosceles triangle | b. Two sides are of equal length |
| 3. Equilateral triangle | c. All three sides are of equal length |
Answer: __________________________________________
Match the term with its corresponding geometric property in triangle geometry.
[2 marks]| Column A | Column B |
|---|---|
| 1. Equilateral Triangle | a. All angles are 60 degrees |
| 2. Right Triangle | b. One angle is 90 degrees |
| 3. Scalene Triangle | c. All sides have different lengths |
| 4. Obtuse Triangle | d. One angle is greater than 90 degrees |
Answer: __________________________________________
In an isosceles triangle ABC where AB = AC, the angles opposite to the equal sides are _____, and the line segment from the vertex A perpendicular to BC bisects the _____.
[2 marks]If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an _____ triangle.
[2 marks]State the condition under which two triangles are congruent by the RHS (Right-angle Hypotenuse Side) criterion.
[2 marks]Define the SSS congruence rule as it applies to two triangles in a geometric proof.
[1 mark]Define an exterior angle of a triangle and state its relationship with the interior opposite angles.
[2 marks]In triangle PQR, angle P = 60 degrees and angle Q = 40 degrees. Determine the measure of angle R and state the theorem used.
[3 marks]Rohan is flying a kite in Jaipur during Makar Sankranti. The string of the kite is 100 m long and it makes an angle of 30° with the horizontal ground. Assuming there is no slack in the string, calculate the height of the kite above the ground.
[3 marks]A ladder 10 meters long reaches a window 8 meters above the ground in a housing society in Mumbai. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 6 meters high. Find the width of the street.
[4 marks]Consider two similar triangles ABC and PQR where angle A = angle P and angle B = angle Q. Identify the correct corresponding proportional side relationship from the choices below.
[2 marks]