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SIMILARITY Worksheet - Solution

The document is an education worksheet focused on similarity in geometry, containing questions and answers related to ratios, areas of similar triangles, and properties of polygons. It includes both short answer questions and true/false statements, along with calculations involving scale factors and area. The total marks for the worksheet are 15, and it is designed to be completed in 25 minutes.

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Akash Chaubey
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417 views3 pages

SIMILARITY Worksheet - Solution

The document is an education worksheet focused on similarity in geometry, containing questions and answers related to ratios, areas of similar triangles, and properties of polygons. It includes both short answer questions and true/false statements, along with calculations involving scale factors and area. The total marks for the worksheet are 15, and it is designed to be completed in 25 minutes.

Uploaded by

Akash Chaubey
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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EDUCATION SPRINT

WORKSHEET Total Marks : 15


Time : 25 Minute
SIMILARITY

Que : 1 (A) Answer The Following Questions In One Sentence. [6]

1. In the following figure, point D divides AB in the ratio 3 : 5. Find : AD

AB

Ans. : Given that AD


=
3

5
DB

So,
AD 3
=
AB 8

2. The ratio between the corresponding sides of two similar triangles is 2 is to 5.


Find the ratio
between the areas of these triangles.

Ans. : We know that the ratio of the areas of two similar triangles is equal to the
ratio of squares of their corresponding sides.
2

Required ratio = 2
2
=
4

5 25

3. Area of two similar triangles are 98 sq.cm and 128 sq.cm. Find the ratio between
the lengths
of their corresponding sides.
−−−
√49
Ans. : Required ratio
98 7
= √ = =
128 64 8

4. A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C'
Calculate : the length of AB, if A' B' = 6 cm.
Ans. : Given that ABC has been enlarged by scale factor m = 2.5 to the triangle A' B'
C'
A' B' = 6cm
So, AB (2.5) = A'B'
⇒ AB (2.5) = 6

⇒ AB = 2.4 cm

Page 1
5. A model of an aeroplane is made to a scale of 1 : 400. Calculate :
the length, in cm, of the model; if the length of the aeroplane is 40 m
Ans. : The ratio of the length of two corresponding sides of two similar triangles.
A model of an aeroplane is made to a scale of 1 : 400.
So, the length of the model = 1
× 4000 = 10cm
400

6. On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the


following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.
Calculate : the area of the plot in sq. km.
Ans. : The area of the plot in sq. km
1
= × AB × BC
2

1
= × 7.5 × 10
2

= 37.5 sq. km

Que : 1 (B) TRUE / FALSE [7]

7. Two similar polygons are necessarily congruent.


Ans. : False
8. Two congruent polygons are necessarily similar.
Ans. : True
9. all equiangular triangles are similar.
Ans. : True
10. all isosceles triangles are similar.
Ans. : False
11. Two isosceles – right triangles are similar
Ans. : True
12. Two isosceles triangles are similar, if an angle of one is congruent to the
corresponding angle of the other.
Ans. : True
13. The diagonals of a trapezium, divide each other into proportional segments.
Ans. : True.

Que : 2 (A) Answer The Following Questions in Brief. [2]

1. In the following figure, ABCD to a trapezium with AB ‖ DC. If AB = 9 cm, DC = 18


cm, CF= 13.5,cm, AP = 6 cm and BE = 15 cm, Calculate: EC

Page 2
Ans. : In ΔAEB and ΔFEC,
∠AEB = ∠FEC ..(Vertically opposite angles)
∠BAE = ∠CFE ....(Since AB || DC)
ΔAEB ∼ ΔAFEC ....(AA criterion for similarity)
AE BE AB
⇒ = =
FE CE FC

15 9
⇒ =
CE 13.5

⇒ CE = 22.5 cm
----- -----

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