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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-07-CT
Triangles — Full Chapter Test
Chapter: Triangles
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
The ratio of areas of similar triangles equals:
  • A.side ratio
  • B.(side ratio)$^2$
  • C.perimeter ratio
  • D.angle ratio
3.
(Hypotenuse)$^2=$
  • A.sum of legs
  • B.sum of squares of legs
  • C.product of legs
  • D.difference of legs
4.
AAA is a criterion for:
  • A.congruence
  • B.similarity
  • C.area
  • D.reflection
5.
Sides ratio $2:3$ gives area ratio:
  • A.$2:3$
  • B.$4:9$
  • C.$8:27$
  • D.$6:9$
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.
Sides are in ratio $3:5$; find the ratio of areas.
8.
Find the hypotenuse if the legs are $5$ and $12$.
9.
State the SSS similarity criterion.
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.
Two similar triangles have areas $81$ cm$^2$ and $144$ cm$^2$; a side of the smaller is $9$ cm. Find the corresponding side of the larger.
12.
A $15$ m ladder leans against a wall reaching $12$ m. How far is its foot from the wall?
13.
$\triangle ABC\sim\triangle DEF$; $AB=6,\ DE=9,\ BC=8$. Find $EF$.
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.
The areas of two similar triangles are $100$ cm$^2$ and $49$ cm$^2$. If the altitude of the bigger is $5$ cm, find the corresponding altitude of the smaller.

Answer Key

Section A — Multiple Choice Questions
  1. (B) proportional
  2. (B) (side ratio)$^2$
  3. (B) sum of squares of legs
  4. (B) similarity
  5. (B) $4:9$
Section B — Short Answer (2 marks)
  1. $1:2$.
  2. $9:25$.
  3. $13$.
  4. All three pairs of corresponding sides are proportional.
Section C — Short Answer (3 marks)
  1. $6$.
  2. $12$ cm.
  3. $9$ m.
  4. $12$.
Section D — Long Answer (5 marks)
  1. $AE=3$ cm.
  2. $3.5$ cm.
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