Question 1:
(i) Prove that is similar to
(ii) Find
(iii) Find [2014]
Answer:
Question 2: In the given triangle are mid points of sides
respectively. Prove that
Answer:
alternate)
Since is the mid point of
Question 3: In the following figure are medians of
Prove that :
Answer:
Question 4: In the given figure
are altitudes where as
are medians. Prove:
Answer:
(Since
are medians
.. … … … (i)
Since
.. … … … (ii)
From (i) and (ii) we get
and
Question 5: Two similar triangles are equal in area. Prove that the triangles are congruent.
Answer:
Let the two triangles be
Since the two triangles are similar, We know
Since the are of the two triangles is equal
Question 6: The ratio between the altitudes of two similar triangles is Write the ratios between their (i) medians (ii) perimeters (iii) areas.
Answer:
The ratio of the altitude of two similar triangles is the same as the ratio of their sides. Given ratio
(i) Ratio between their median
(ii) Ratio between their perimeter
(iii) Ratio between their areas
Question 7: The ratio between the altitudes of two similar triangles is Find the ratio between their: (i) perimeters (ii) altitudes (iii) medians
Answer:
The ratio between the altitudes of two similar triangles is
This means that the ratio of the sides of the triangles = 4:5
(i) Ratio between their perimeter
(ii) Ratio between their altitude
(iii) Ratio between their median
Question 8: The following figure shows a in which
If
, find the length of
Answer:
Question 9: In the following figure, are parallel lines.
Calculate:
[1985]
Answer:
Now
Also
Question 10: On a map, drawn to a scale of , a rectangular plot of land
has
Calculate:
(i) the diagonal distance of the plot in km
(ii) the area of the plot
Answer:
Length of AB on map actual length of AB
Actual length of
Similarly Actual length of
(i) Therefore the diagonal
(ii) Area of the plot
Question 11: The dimension of a model of a multi storied building are by
by
If the scale factor is
, find the actual dimensions of the building. Also find:
(i) the floor area of a room of the building, if the floor area of the corresponding room in the model is
(ii) the space inside the room of the model if the space inside the corresponding room if the building is
Answer:
Dimension of model
Question 12: are two points on the base
, such that
Prove that:
[2003]
Answer:
Question 13:
$latex \displaystyle \text{Prove that: } \frac{BC^2}{AC^2} = \frac{BD}{AD} . $
Answer:
(Common)
.. … … … (ii)
(Common)
.. … … … (ii)
From (i) and (ii)
Hence Proved.
Question 14: A with
is enlarged to a
such that the longest side of
Find the scale factor and hence, the lengths of the other sides of
Answer:
Question 15: Two isosceles triangles have equal vertical angles. Show that the triangles are similar. If the ratio between the areas of these two triangles is , find the ratio between their corresponding altitudes.
Answer:
(Common)
Question 16: and is extended to
so that
Find:
Answer:
Question 17:The following figure shows a
in which
Show that:
Answer:
Question 18: In the given figure,
is a triangle with
Prove that
If
and area of
Calculate the:
(i) length of (ii) area of
[2010]
Answer:
(common)
Area of
Question 19: In the given figure
is a right angled triangle with
(i) Prove
(ii) If , find
(iii) Find the ratio of the area of is to area of
[2011]
Answer:
Question 20: In the given figure
are perpendiculars to
(i) Prove that
(ii) If , calculate
(iii) Find the ratio of the [2013]
Answer:
,
Therefore the