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