Q1. If in two right triangles, hypotenuse and one side of one
triangle are proportional to the hypotenuse and one side of the other
triangle,then the two triangles are __________.
Both
similar and congruent
Similar
Congruent
Neither
similar nor congruent
Q2. Two equilateral triangles are
always
similar
never
similar
cannot
say unless measurements are given
only
if they are congruent
Q3. Triangle ABC is similar to triangle DEF and their areas
are 64 cm2 and 121 cm2 respectively. If EF=
15.4 cm, then BC = ?
11
cm
8
cm
13
cm
11.2
cm
Q4. The ratio of the areas of two similar triangles is equal
to the:
square
of the ratio of their corresponding sides.
the
ratio of their corresponding sides
square
of the ratio of their corresponding angles
None
Q5. "A line from midpoint of one side of a triangle,
parallel to second side bisects the third side." is the statement of:
converse
of mid point theorem
converse
of basic proportionality theorem
mid
point theorem
basic
proportionality theorem
Q6. A vertical stick 30 m long casts a shadow 15 m long on
the ground. At the same time, a tower casts a shadow 75 m long on the ground.
The height of the tower is:
150
m
100
m
25
m
200
m
Q7. A wood frame for pouring concrete has an interior
perimeter of 14 metres. Its length is one metre greater than its width. The
frame is to be braced with twelve-gauge steel cross-wires. Assuming an extra
half-metre of wire is used at either end of a cross-wire for anchoring, what
length of wire should be cut for each brace?
6
m
14
m
60
m
4
m
Q8. ∆ABC and ∆XYZ are similar, and if AB =11 cm, XY= 7 cm and
BC = 22 cm, then YZ =
14
15
16
none
of these
Q9. Given that ΔABC~ΔDEF and AB = 2 cm, BC = 3 cm, DE =
4 cm, EF = 6 cm. If DF = 8 cm, then AC = ?
5
cm
4
cm
3
cm
8
cm
Q10. If the sum of the length of the legs of a right triangle
is 49 cm and the hypotenuse is 41 cm, find its shortest side.
19
cm
9
cm
40
cm
4
cm
Q11. A Pythagorean triplet is 7, 24, X. What is the value of
X?
25
75
48
28
Q12. If the ratios of areas of two similar triangles are 169:
225 the ratios of their corresponding angle-bisector segments is:
5
: 4
13
: 15
13
: 5
15
: 13
Q13. If two or more figures are similar, their sizes can be
compared. The________ is the ratio of the length of one side on one figure to
the length of the corresponding side on the other figure.
scale
factor
constant
proportionality
constant
of proportionality
Q14. What is the diagonal length of a TV screen whose
dimensions are 80 x 60 cm?
10
100
1000
20
Q15. In right triangle ABC right angled at B ,a line DE is
drawn through the mid point D of AB and parallel to BC. If AB=9 cm, BC=12 cm.
AE=?
7.5
cm
10
cm
13
cm
8.5
cm
Q16. In ΔPQR, A and B are points on PQ, PR such that PA=4
,PB=3, AQ = 8,BR = 6, then AB and QR are :
Intersecting
lines
Parallel
lines
Same
line
Q17. If the legs of an isosceles right triangle are 5 cm
long, approximate the length of the hypotenuse to the nearest whole number.
7
cm
9
cm
70
cm
90
cm
Q18. Three squares are based on the sides of a right angled
triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What
is the area of the third one?
400
sq. cm
625
sq. cm
900
sq. cm
361
sq. cm
Q19. Two congruent triangles are actually similar triangles
with the ratio of corresponding sides as
1:2
1:1
2:1
1:3
Q20. If the ratios of areas of two similar triangles are 121
: 49 the ratios of their corresponding angle-bisector segments is :
5
: 4
11
: 7
4
: 5
625
: 256
Q21. There is a building with window at a height of 12 m. You
want to use a ladder to go up to the window, and you decide to keep the ladder
5 m away from the building to have a good slant. How long should the ladder be?
25
m
12
m
13
m
169
m
Q22. In a triangle ABC, BC ||DE If AD=1.5,DB=4.5,AE=1.3,EC=?
2.6
3.9
3
3.6
Q23. Which geometric figures are always similar?
Circles
and triangles
Circles
Regular
polygons
Circles
and all regular polygons
Q24. In triangle PQR, ST is a line intersecting PQ and PR in
S and T respectively such that ST ||QR. If PS=x, SQ=2,PT=x+3,TR=x-3.What
is the value of x?
9
4
6
8
Q25. If the ratio of the perimeters of two similar triangles
ABC and DEF is 3:7 . What is the ratio of their corresponding sides?
3:5
3:7
2:3
1:7
Q26. If the sum of the squares of a and b is the same as the
square of c and if m < n, then for what value of k can the Pythagorean
triples be generated with the following equations? a = n2 + k ,
b = 2mn : c = m2 + n2
-
m2
m2
-n2
m
Q27. In ΔABC, DE || BC AD=3 cm, DB=8 cm AC=22 cm. At what
distance from A does the line DE cut AC?
5
4
6
10
Q28. If a line divides any two sides of a triangle in the
same ratio, then ______________
It
will intersect the third side
It
divides the third side in the same ratio
It
is parallel to the third side
It
is not possible
Q29. ΔABC~ΔDEF. Perimeter(ΔABC) = 15 cm, perimeter(ΔDEF) = 25
cm. If AB= 6 cm, then find DE.
12
14
10
16
Q30. Sides of two similar triangles are in the ratio 4: 9.
What is the ratio of the area of these triangles?
2:3
4:9
81:
16
16:
81
Q31. In ΔDEF, GH is a line parallel to EF cutting DE in
G and and DF in H. If DE=16.5, DH=5, HF=6, GE=?
9
10
8
7.5
Q32. Out of the following which one is an application of the
Pythagoras theorem?
Distance
formula
Section
formula
Mid-point
formula
Area
of a triangle formula
Q33. A line PQ divides the sides XY and XZ of a ΔXYZ in two
parts such that XP = 1.8 cm, PY = 3.6 cm, XQ = 0.8 cm and QZ = 1.6 cm. By
applying the ………… theorem, it can be said that PQ||YZ.
Basic
Proportionality
Converse
of Basic Proportionality
Pythagoras
Converse
of Pythagoras
Q34. Which of the following is a Pythagorean triplet?
(36,18,43)
(15,20,25)
(3,12,13)
(24,25,26)
Q35. Two poles stand on the ground at a distance of 20m and
50 m respectively from a point A on the ground, the taller pole at 30 m from
smaller pole. A cable originates from the top pf the taller pole, passing on
the other pole ends on a hook at point A. If the length of the cable is 100 m ,
how much of it lies between the the two poles?
60
m
50m
80m
40
m
Q36. Three numbers form a Pythagorean triplet. Two of them
are 15 and 17 where 17 is the largest of them. The third number is
5
8
13
12
Q37. P and Q are points on sides AB and AC, respectively, of
∆ABC. If AP = 4 cm, PB = 12 cm, AQ = 2 cm and QC = 6 cm, then BC =
4PQ
3PQ
2PQ
PQ
Q38. In the given figure AD=2 cm, DB=5 cm AC=21 cm and DE ll
BC. Find AE =?
5
7
6
8
Q39. A vertical pole of 10 m casts a shadow of 6 m long on
the ground. At the same time, a tree casts a shadow 60 m long on the ground.
The height of the tree is
100
m
120
m
25
m
200
m
Q40. Two friends A and B start from the same point in the Eastern
and Northern directions at the same time. How far are they from each other when
A has travelled 5 km and B has travelled 12 km. distance?
17
km
10
km
13
km
8
km
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