Free printable worksheet
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?
[1 mark]Which of the following conditions is NOT sufficient to prove that two triangles are congruent?
[1 mark]Match each quadratic expression with its correct factorised form.
[2 marks]| Column A | Column B |
|---|---|
| 1. $x^2 + 6x + 9 | a. (x+3)^2$ |
| 2. $x^2 - 9 | b. (x+3)(x-3)$ |
| 3. $x^2 - 6x + 9 | c. (x-3)^2$ |
| 4. $x^2 - 5x + 6 | d. (x-2)(x-3)$ |
Answer: __________________________________________
Match each pair of triangle congruence criteria with its correct description.
[2 marks]| Column A | Column B |
|---|---|
| 1. SSS | a. All three sides of one triangle are equal to all three sides of the other triangle. |
| 2. SAS | b. Two sides and the included angle of one triangle are equal to two sides and the included angle of the other. |
| 3. RHS | c. The hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another. |
Answer: __________________________________________
Match each given pair of triangle conditions to the correct congruence test.
[3 marks]| Column A | Column B |
|---|---|
| 1. Two angles and the included side are equal | a. ASA |
| 2. Two sides and the included angle are equal | b. SAS |
| 3. All three corresponding sides are equal | c. SSS |
| 4. Hypotenuse and one side of right triangles are equal | d. RHS |
Answer: __________________________________________
When we factorise the algebraic expression $5x + 15$ by taking out the common factor, we get $5($____$)$.
[1 mark]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.
[1 mark]Define what is meant by 'factorising an algebraic expression' in your own words.
[2 marks]State the condition under which two right-angled triangles are congruent if their hypotenuse and one side are equal.
[2 marks]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.
[3 marks]Factorise the following expression by grouping: $x^2 - xz + xy - yz$.
[3 marks]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.
[3 marks]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.
[3 marks]Examine the reference diagram showing intersecting line segments forming two triangles. Identify the correct labels for the marked vertices A, B, C, D, and O in standard triangle notation.
[3 marks]