Class 10 Triangles Mock Test (CBSE)

Topics in Triangles

• Similar figures
• Similarity of triangles
• Basic proportionality theorem
• Criteria for similarity of triangles

Triangles practice questions with answers

1. Q1Multiple choice·1 mark
   In $\triangle ABC$ and $\triangle DEF$, $\frac{AB}{DE} = \frac{BC}{FD}$. These two triangles will be similar by SAS criterion if:

   1. (a)$\angle A = \angle D$
   2. (b)$\angle B = \angle E$
   3. (c)$\angle B = \angle D$
   4. (d)$\angle A = \angle C$
   Show answer and step marks

   1. Correct option: (c) $\angle B = \angle D$+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   In $\triangle ABC$, $DE \parallel BC$ with $D$ on $AB$ and $E$ on $AC$. If $\frac{AD}{DB} = \frac{3}{5}$ and $AC = 5.6\text{ cm}$, then the length of $AE$ is:

   1. (a)$2.1\text{ cm}$
   2. (b)$3.5\text{ cm}$
   3. (c)$2.8\text{ cm}$
   4. (d)$1.4\text{ cm}$
   Show answer and step marks

   1. Correct option: (a) $2.1\text{ cm}$. By BPT, $\frac{AD}{AD+DB} = \frac{AE}{AE+EC} \implies \frac{3}{3+5} = \frac{AE}{5.6} \implies AE = \frac{3 \times 5.6}{8} = 2.1\text{ cm}$.+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   If $\triangle ABC \sim \triangle PQR$ such that $\frac{AB}{PQ} = \frac{1}{3}$, then the ratio of the area of $\triangle ABC$ to the area of $\triangle PQR$ is:

   1. (a)$\frac{1}{3}$
   2. (b)$\frac{1}{9}$
   3. (c)$\frac{1}{27}$
   4. (d)$3$
   Show answer and step marks

   1. Correct option: (b) $\frac{1}{9}$, as the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: $\left(\frac{1}{3}\right)^2 = \frac{1}{9}$.+1

   Answer: (b)
4. Q4Short answer·3 marks
   In $\triangle ABC$ and $\triangle DEF$, the sides are $AB = 4.5$ cm, $BC = 6$ cm, $CA = 7.5$ cm, and $DE = 6$ cm, $EF = 8$ cm, $FD = 10$ cm. (a) State the criterion of similarity that applies when the three pairs of corresponding sides of two triangles are proportional. [1] (b) Find the common value of $\frac{AB}{DE}$, $\frac{BC}{EF}$ and $\frac{CA}{FD}$. [1] (c) Write the similarity statement for $\triangle ABC$ and $\triangle DEF$, with the vertices written in the correct order. [1]
   Show answer and step marks

   1. (a) The criterion is the SSS (side-side-side) similarity criterion: if corresponding sides of two triangles are proportional, the triangles are similar.+1
   2. (b) $\frac{AB}{DE} = \frac{4.5}{6} = \frac{3}{4}$, $\frac{BC}{EF} = \frac{6}{8} = \frac{3}{4}$ and $\frac{CA}{FD} = \frac{7.5}{10} = \frac{3}{4}$, so the common value is $\frac{3}{4}$.+1
   3. (c) Since all three ratios are equal, $\triangle ABC \sim \triangle DEF$.+1

   Answer: (a) SSS similarity criterion; (b) $\frac{3}{4}$; (c) $\triangle ABC \sim \triangle DEF$

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