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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-07-SIM-01
Similar Figures & Criteria — Assignment
Chapter: Triangles
Topic: Similar Figures and Criteria of Similarity
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Similar triangles have corresponding sides:
  • A.equal
  • B.proportional
  • C.perpendicular
  • D.parallel
2.
AAA is a criterion for:
  • A.congruence
  • B.similarity
  • C.area
  • D.reflection
3.
All circles are:
  • A.congruent
  • B.similar
  • C.equal
  • D.different
4.
If $\triangle ABC\sim\triangle DEF$, then $\tfrac{AB}{DE}=$
  • A.$\tfrac{AC}{DF}$
  • B.$\tfrac{DF}{AC}$
  • C.$1$
  • D.$\tfrac{BC}{DF}$
5.
Congruent triangles are always:
  • A.larger
  • B.similar
  • C.right-angled
  • D.unequal
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $\triangle ABC\sim\triangle PQR$ with $AB=4,\ PQ=8$, find the ratio of similarity.
7.
State the SSS similarity criterion.
8.
Two similar triangles have ratio $2:3$. Find the ratio of perimeters.
9.
Are all equilateral triangles similar?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $\triangle ABC$, $DE\parallel BC$ with $AD=2,\ DB=3,\ AE=4$. Find $EC$.
11.
$\triangle ABC\sim\triangle DEF$; $AB=6,\ DE=9,\ BC=8$. Find $EF$.
12.
State the Basic Proportionality (Thales) Theorem.
13.
Two similar triangles have perimeters $30$ and $45$; a side of the first is $10$. Find the corresponding side.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In $\triangle ABC$, $DE\parallel BC$ meets $AB$ at $D$ and $AC$ at $E$. If $\tfrac{AD}{DB}=\tfrac35$ and $AC=8$ cm, find $AE$.
15.
In a trapezium $ABCD$ with $AB\parallel DC$, the diagonals meet at $O$. Show that $\tfrac{AO}{OC}=\tfrac{BO}{OD}$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) proportional
  2. (B) similarity
  3. (B) similar
  4. (A) $\tfrac{AC}{DF}$
  5. (B) similar
Section B — Short Answer (2 marks)
  1. $1:2$.
  2. All three pairs of corresponding sides are proportional.
  3. $2:3$.
  4. Yes.
Section C — Short Answer (3 marks)
  1. $6$.
  2. $12$.
  3. A line parallel to one side divides the other two sides proportionally.
  4. $15$.
Section D — Long Answer (5 marks)
  1. $AE=3$ cm.
  2. $\tfrac{AO}{OC}=\tfrac{BO}{OD}$.
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