Vidaara.orgClass 10 · Mathematics
CodeVID-M10-07-CT
Triangles — Full Chapter Test
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
- (B) proportional
- (B) (side ratio)$^2$
- (B) sum of squares of legs
- (B) similarity
- (B) $4:9$
Section B — Short Answer (2 marks)
- $1:2$.
- $9:25$.
- $13$.
- All three pairs of corresponding sides are proportional.
Section C — Short Answer (3 marks)
- $6$.
- $12$ cm.
- $9$ m.
- $12$.
Section D — Long Answer (5 marks)
- $AE=3$ cm.
- $3.5$ cm.
Generated by Vidaara.org · Assignment VID-M10-07-CT · vidaara.org