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# NCERT Solutions, Exercise 6.4, Triangles, Class 10 (Mathematics) Class 10 Notes | EduRev

## Class 10 : NCERT Solutions, Exercise 6.4, Triangles, Class 10 (Mathematics) Class 10 Notes | EduRev

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Mathematics
(Chapter – 6) (Triangles)
(Class – X)

1

Exercise 6.4
Question 1:
Let and their areas be, respectively, 64 cm
2
and 121 cm
2
. If EF =
15.4 cm, find BC.

Page 2

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

1

Exercise 6.4
Question 1:
Let and their areas be, respectively, 64 cm
2
and 121 cm
2
. If EF =
15.4 cm, find BC.

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

2

Question 2:
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB
= 2CD, find the ratio of the areas of triangles AOB and COD.

Since AB || CD,
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)
In ?AOB and ?COD,
?AOB = ?COD (Vertically opposite angles)
?OAB = ?OCD (Alternate interior angles)
?OBA = ?ODC (Alternate interior angles)
? ?AOB ~ ?COD (By AAA similarity criterion)

Page 3

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

1

Exercise 6.4
Question 1:
Let and their areas be, respectively, 64 cm
2
and 121 cm
2
. If EF =
15.4 cm, find BC.

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

2

Question 2:
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB
= 2CD, find the ratio of the areas of triangles AOB and COD.

Since AB || CD,
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)
In ?AOB and ?COD,
?AOB = ?COD (Vertically opposite angles)
?OAB = ?OCD (Alternate interior angles)
?OBA = ?ODC (Alternate interior angles)
? ?AOB ~ ?COD (By AAA similarity criterion)

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

3
Question 3:
In the following figure, ABC and DBC are two triangles on the same base BC. If AD

Let us draw two perpendiculars AP and DM on line BC.

In ?APO and ?DMO,
?APO = ?DMO (Each = 90°)
?AOP = ?DOM (Vertically opposite angles)
? ?APO ~ ?DMO (By AA similarity criterion)

intersects BC at O, show that

We know that area of a triangle =
.
Page 4

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

1

Exercise 6.4
Question 1:
Let and their areas be, respectively, 64 cm
2
and 121 cm
2
. If EF =
15.4 cm, find BC.

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

2

Question 2:
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB
= 2CD, find the ratio of the areas of triangles AOB and COD.

Since AB || CD,
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)
In ?AOB and ?COD,
?AOB = ?COD (Vertically opposite angles)
?OAB = ?OCD (Alternate interior angles)
?OBA = ?ODC (Alternate interior angles)
? ?AOB ~ ?COD (By AAA similarity criterion)

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

3
Question 3:
In the following figure, ABC and DBC are two triangles on the same base BC. If AD

Let us draw two perpendiculars AP and DM on line BC.

In ?APO and ?DMO,
?APO = ?DMO (Each = 90°)
?AOP = ?DOM (Vertically opposite angles)
? ?APO ~ ?DMO (By AA similarity criterion)

intersects BC at O, show that

We know that area of a triangle =
.
Mathematics
(Chapter – 6) (Triangles)
(Class – X)

4
Question 4:
If the areas of two similar triangles are equal, prove that they are congruent.

Let us assume two similar triangles as ?ABC ~ ?PQR.

Question 5:
D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio
of the area of ?DEF and ?ABC.

D and E are the mid-points of ?ABC.
Page 5

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

1

Exercise 6.4
Question 1:
Let and their areas be, respectively, 64 cm
2
and 121 cm
2
. If EF =
15.4 cm, find BC.

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

2

Question 2:
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB
= 2CD, find the ratio of the areas of triangles AOB and COD.

Since AB || CD,
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)
In ?AOB and ?COD,
?AOB = ?COD (Vertically opposite angles)
?OAB = ?OCD (Alternate interior angles)
?OBA = ?ODC (Alternate interior angles)
? ?AOB ~ ?COD (By AAA similarity criterion)

Mathematics
(Chapter – 6) (Triangles)
(Class – X)

3
Question 3:
In the following figure, ABC and DBC are two triangles on the same base BC. If AD

Let us draw two perpendiculars AP and DM on line BC.

In ?APO and ?DMO,
?APO = ?DMO (Each = 90°)
?AOP = ?DOM (Vertically opposite angles)
? ?APO ~ ?DMO (By AA similarity criterion)

intersects BC at O, show that

We know that area of a triangle =
.
Mathematics
(Chapter – 6) (Triangles)
(Class – X)

4
Question 4:
If the areas of two similar triangles are equal, prove that they are congruent.

Let us assume two similar triangles as ?ABC ~ ?PQR.

Question 5:
D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio
of the area of ?DEF and ?ABC.

D and E are the mid-points of ?ABC.
Mathematics
(Chapter – 6) (Triangles)
(Class – X)

5

Question 6:
Prove that the ratio of the areas of two similar triangles is equal to the square  of
the ratio of their corresponding medians.

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