Class 9 · Mathematics · 10 Aug 2026

Which congruence criterion is NOT sufficient to prove that two triangles are congruent?

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.

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?

Match each type of triangle with its defining property regarding sides.

Match the term with its corresponding geometric property in triangle geometry.

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 _____.

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an _____ triangle.

State the condition under which two triangles are congruent by the RHS (Right-angle Hypotenuse Side) criterion.

Define the SSS congruence rule as it applies to two triangles in a geometric proof.

Define an exterior angle of a triangle and state its relationship with the interior opposite angles.

In triangle PQR, angle P = 60 degrees and angle Q = 40 degrees. Determine the measure of angle R and state the theorem used.

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.

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.