List of top Mathematics Questions on Triangles

Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that $AQ = QR$.

In the given figure, $ \triangle AHK \sim \triangle ABC $. If $ AK = 10 \text{ cm} $, $ BC = 3.5 \text{ cm} $ and $ HK = 7 \text{ cm} $, find the length of $ AC $.

In the same figure as 32(a), prove that $EF \parallel BC$.

D is the mid-point of side BC of $\triangle ABC$. CE and BF intersect at O, a point on AD. AD is produced to G such that $OD = DG$. Prove that OBGC is a parallelogram.

In the given figure, $ XY \parallel QR $, $ \frac{PQ}{XQ} = \frac{7}{3} $ and $ PR = 6.3 \text{ cm} $. Find the length of $ YR $.

In the given figure, $\Delta AHK \sim \Delta ABC$. If $AK = 10 \text{ cm}$, $BC = 3.5 \text{ cm}$ and $HK = 7 \text{ cm}$, find the length of $AC$.

Using the conditions from 32(b), prove that $PR = 2AP$.

In triangles ABC and PQR, $ \angle A = \angle Q $ and $ \angle B = \angle R $, then $ AB : AC $ is equal to :

In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\triangle ABC \sim \triangle DEF$. If $BC = 10$ cm, $EB = CF = 5$ cm and $AB = 7$ cm, then find the length DE.

$ABCD$ is a parallelogram such that $AF = 7 \text{ cm}$, $FB = 3 \text{ cm}$ and $EF = 4 \text{ cm}$, length $FD$ equals

let mid "“ point of sides of $\Delta$ are $(\frac{5}{2}, 3), (\frac{5}{2}, 7) \, \& \, (4, 5)$. If incentre is $(h, k)$ then value of $3h + k$ is:

In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.

What is the height of the tower ?

Draw a rough sketch showing these details.

A circle is drawn with line joining the points (3, 5) and (5, 9) as diameter.

From the top of a mobile tower, two steel wires are stretched to either side and attached to the ground, making angles 70° and 48°. The distance between the feet of the wires is 40 metres.

Calculate the area of triangle ABC.

In the figure one side of the triangle is 10 centimetres and angles on that side are 60° and 45°. Calculate the area of the triangle.

A toy is in the shape of a square pyramid of base edge 18 centimetres and height 12 centimetres. What is the total cost of painting 500 such toys at 120 rupees per square metre ?

Draw a circle of radius 2.5 centimetres. Draw a triangle of two angles 70° and 50° with its sides touches the circle.

Draw a triangle of circum radius 3 centimetres and two of the angles 75° and 50°.

Draw a rectangle of area 18 square centimetres and a square of same area.

The base radius and height of a solid metal cylinder are 8 centimetres and 15 centimetres. By melting it and recasting, how many cones of base radius 6 centimetres and slant height 10 centimetres can be made ?

The altitude of a right triangle is 35 cm less than its base. If the hypotenuse is 65 cm, find the other two sides.

In the figure ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Prove that $\frac{AE}{ED} = \frac{BF}{FC}$.