Chapter 6 · Model TestAttempt first – solutions on the next page

Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ

Set a timer for 1½ hours, keep the textbook closed, and write your answers in a notebook. Then check them on the solved paper, which also shows how marks are given.

(the navigation bars are left out when printing)

Kerala State Syllabus · Standard IX

MATHEMATICS – Chapter 6: Similar Triangles (സദൃശത്രികോണങ്ങൾ)

Time: 1½ hoursMaximum marks: 40
Instructions: Read each question carefully. Rough figures are enough unless a construction is asked for. Show your working – marks are given for correct steps even when the final answer is wrong. Section A: 8 × 1 = 8, Section B: 5 × 2 = 10, Section C: 4 × 3 = 12, Section D: 2 × 5 = 10.
SECTION A – Answer all questions8 × 1 = 8 marks
1.
Two triangles have the same angles 40°, 60° and 80°. The side opposite the 80° angle is 6 cm in the first triangle and 9 cm in the second. The scale factor from the first triangle to the second is .
(1)
2.
In ΔPQR, ∠P = 70°, ∠Q = 60° and ∠R = 50°. The longest side of the triangle is
(a) PQ(b) QR(c) PR(d) all sides are equal
(1)
3.
If every side of a triangle is multiplied by 3, its area is multiplied by .
(1)
4.
Which pair of triangles need not be similar?
(a) two equilateral triangles(b) two right triangles each having an angle of 30°(c) two isosceles triangles(d) a triangle with sides 3, 4, 5 cm and one with sides 6, 8, 10 cm
(1)
5.
The perpendicular from the right-angle vertex of a right triangle divides the hypotenuse into parts of 4 cm and 9 cm. The length of the perpendicular is cm.
(1)
6.
In the figure, DE is parallel to BC. AD = 2 cm, DB = 4 cm and AE = 3 cm. Then EC = cm.
(1)
7.
Fill in the blank: "Triangles with the same angles have their sides, taken in order of size, in the same ."
(1)
8.
In ΔABC and ΔPQR, ∠A = ∠P and ∠B = ∠Q. If AB = 5 cm, PQ = 10 cm and BC = 7 cm, then QR =
(a) 3.5 cm(b) 7 cm(c) 14 cm(d) 12 cm
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
The sides of ΔABC are AB = 6 cm, BC = 9 cm and CA = 12 cm. ΔPQR has the same angles as ΔABC, and its shortest side is 4 cm. Find the other two sides of ΔPQR.
(2)
10.
The sides of one triangle are 5 cm, 7 cm and 9 cm; the sides of another are 7.5 cm, 10.5 cm and 13.5 cm. Are the two triangles similar? Give the reason.
(2)
11.
Two poles of heights 6 m and 3 m stand vertically on level ground. A rope is tied from the top of each pole to the foot of the other. At what height above the ground do the two ropes cross?
(2)
12.
In ΔABC, AB = 8 cm, AC = 6 cm and BC = 7 cm. The bisector of ∠A meets BC at P. Find BP and PC.
(2)
13.
The area of a triangle is 24 sq cm.
  1. What is the area of the triangle whose sides are half the sides of this triangle?
  2. What is the area if the sides are made 1½ times?
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
A vertical stick of height 1.5 m casts a shadow 2 m long. At the same time a coconut tree casts a shadow 16 m long.
  1. Draw a rough figure and explain why the two triangles have the same angles.
  2. Find the height of the tree.
(3)
15.
In the figure, a square is drawn inside a right triangle with legs 6 cm and 3 cm: one vertex of the square is at the right-angle corner and the other three vertices lie on the sides. Find the length of a side of the square.
(3)
16.
Two sides of a triangle are 4 cm and 6 cm and the angle between them is 50°. In another triangle two sides are 6 cm and 9 cm and the angle between them is also 50°.
  1. Are the triangles similar? Which rule tells you so?
  2. The third side of the first triangle is 4.6 cm. Find the third side of the second triangle.
(3)
17.
A rectangle has sides 4 cm and 6 cm. A parallelogram has sides 6 cm and 9 cm and angles 60° and 120°.
  1. Are the sides of the two figures in the same ratio?
  2. Are the two figures similar?
  3. What does this show about quadrilaterals compared with triangles?
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
In the figure, ΔABC is right-angled at C and CD is perpendicular to AB. AD = 4 cm and DB = 9 cm.
  1. Prove that ΔADC and ΔCDB have the same angles.
  2. Find CD.
  3. Find AC and BC.
  4. Find the area of ΔABC.
(5)
19.
  1. Describe how to draw ΔABC with AB = 6 cm, BC = 5 cm and CA = 4 cm.
  2. Describe how to draw a triangle whose sides are 1¼ times the sides of ΔABC by measuring its sides.
  3. Describe how to draw the same enlarged triangle using the circumcircle of ΔABC and a second circle, without measuring any side. Explain why the sides of the triangle obtained are 1¼ times the sides of ΔABC.
(5)

— End of the paper —

📝 After the test

Check your answers on the next page. Give yourself marks honestly using the marking hints there. Anything below 28/40 means the chapter needs one more round – the solved paper tells you exactly which page to revisit for each question.

Next: Model Test Paper – Solved ▶