Class 8 · Mathematics · 10 Aug 2026

Aarav has two triangular garden tiles, PQR and XYZ, where PQ = XY, PR = XZ, and \u2220P = \u2220X. Which criterion proves triangle PQR \u2245 triangle XYZ?

Which of the following conditions is NOT sufficient to prove that two triangles are congruent?

Match each quadratic expression with its correct factorised form.

Match each pair of triangle congruence criteria with its correct description.

Match each given pair of triangle conditions to the correct congruence test.

When we factorise the algebraic expression $5x + 15$ by taking out the common factor, we get $5($____$)$.

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent by the _____ criterion.

Define what is meant by 'factorising an algebraic expression' in your own words.

State the condition under which two right-angled triangles are congruent if their hypotenuse and one side are equal.

Analyze the error in the following student work: Student statement: Factorise x² - 5x + 6. Student work: x² - 5x + 6 = (x + 2)(x + 3). Identify the mistake and provide the correct factorisation.

Factorise the following expression by grouping: $x^2 - xz + xy - yz$.

Aarav is designing a rectangular rangoli block on the floor of his living room in Bengaluru. The total area of the block is represented by the expression 12x^2 + 18x square centimetres. If the width of the rectangle is 6x centimetres, find the length of the rectangle by factoring out the common factor.

A rectangular community garden in Bengaluru has an area represented by the algebraic expression $(x^2 + 9x + 20)$ square metres. Factorise this quadratic expression to find possible binomial expressions for its length and breadth.