List of top Mathematics Questions on Triangles asked in CBSE Class X

In the adjoining figure, $PQ \parallel XY \parallel BC$, $AP=2\ \text{cm}, PX=1.5\ \text{cm}, BX=4\ \text{cm}$. If $QY=0.75\ \text{cm}$, then $AQ+CY =$

The perimeters of two similar triangles are 22 cm and 33 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.

Assertion (A) : $\triangle ABC \sim \triangle PQR$ such that $\angle A = 65^\circ$, $\angle C = 60^\circ$. Hence $\angle Q = 55^\circ$.
Reason (R) : Sum of all angles of a triangle is $180^\circ$.

In the adjoining figure, $ \triangle CAB $ is a right triangle, right angled at A and $ AD \perp BC $. Prove that $ \triangle ADB \sim \triangle CDA $. Further, if $ BC = 10 \text{ cm} $ and $ CD = 2 \text{ cm} $, find the length of } $ AD $.

If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.

In the adjoining figure, $ AP = 1 \, \text{cm}, \ BP = 2 \, \text{cm}, \ AQ = 1.5 \, \text{cm}, \ AC = 4.5 \, \text{cm} $ Prove that $ \triangle APQ \sim \triangle ABC $.
Hence, find the length of $ PQ $, if $ BC = 3.6 \, \text{cm} $.

In the adjoining figure, if $\dfrac{AD}{BD} = \dfrac{AE}{EC}$ and $\angle BDE = \angle CED$, prove that $\triangle ABC$ is an isosceles triangle.

In the given figure, AB $||$ DE and BD $||$ EF. Prove that $DC^2 = CF \times AC$.

AB || DE and BD || EF. Prove that DC2 = CF ×AC

A triangular window of a building is shown above. Its diagram represents a $\triangle ABC$ with $\angle A = 90^\circ$ and $AB = AC$. Points P and R trisect AB and $PQ \parallel RS \parallel AC$.

Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

$D$ is a point on the side $BC$ of $\triangle ABC$ such that $\angle ADC = \angle BAC$. Show that:
$AC^2 = BC \times DC$

Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

$D$ is a point on the side $BC$ of $\triangle ABC$ such that $\angle ADC = \angle BAC$. Show that:
$AC^2 = BC \times DC$

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, proves that $\frac{AB}{PQ}=\frac{AD}{PM}$

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC∼ΔPQR

D is a point on the side BC of a triangle ABC such that $\angle$ADC = $\angle$BAC. Show that CA²=CB.CD

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ∼ ∆ECF