List of top Mathematics Questions on Triangles asked in UP Board X

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 $\frac{AE}{ED} = \frac{BF}{FC}$. 

 

In the above figure, if $AD = 2.0$ cm, $AE = 1.8$ cm, $EC = 3.6$ cm and $DE \parallel BC$ the measure of $BD$ will be : 

 

In the following statements, the true statement is :
Prove that if a straight line is drawn parallel to one side of a triangle to intersect the other two sides in two distinct points, then the other two sides are divided by those points in the same ratio.
$D$ is a point on the side $BC$ of a triangle $ABC$ such that $\angle ADC = \angle BAC$. Prove that $CA^2 = CB \cdot CD$.

In the figure, in $\triangle MNL$ and $\triangle PQR$, $\angle M = \angle Q = 70^\circ$, $MN = 3$ cm, $ML = 4.5$ cm, $PQ = 2$ cm, and $QR = 3$ cm. Then, the following correct relation will be: 

In the figure, if \(DE \parallel BC\), then the measure of \(CE\) will be: 

If \(\dfrac{AO}{OC} = \dfrac{BO}{OD} = \dfrac{1}{2}\) and \(AB = 5 \, \text{cm}\) in the following figure, then find the value of \(DC\). 

In the figure, there is a pair of similar triangles. Its correct symbolic expression will be 

In the given figure, if \( ST \parallel QR \), \( QS = 3 \text{ cm} \), \( SR = 1.5 \text{ cm} \), and \( PT = 2.8 \text{ cm} \), then find the value of \( TR \). 

In the figure, if $LM \parallel CB$ and $LN \parallel CD$, then prove that $\dfrac{AM}{BM} = \dfrac{AN}{DN}$. 

If in $\triangle ABC$ and $\triangle DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then they will be similar if
Two triangles are said to be similar to each other:
D is a point on the side BC of a triangle ABC such that \( \angle ADC = \angle BAC \). Prove that \( CA^2 = CB \times CD \).
$\triangle ABC$ is an equilateral triangle of side $2a$. The length of each of its altitudes will be:
Prove that the line dividing any two sides of a triangle in a same ratio is parallel to the third side of the triangle.
If AD \(\perp\) BC in an equilateral triangle ABC, then AD\(^2\) will be
If ABC and XYZ are two similar triangles and \(\angle A = 75^\circ\) and \(\angle Y = 57^\circ\), then the value of \(\angle C\) will be
Construct \( \triangle ABC \), in which \( BC = 6 \, \text{cm} \), \( AB = 4.5 \, \text{cm} \) and \( \angle ABC = 60^\circ \). Then construct another triangle whose sides are \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \).
In the given figure, \( DE \) is drawn parallel to base \( BC \) of triangle \( ABC \). If \( DB = 7.2 \) cm, \( AE = 1.8 \) cm, and \( EC = 5.4 \) cm, then the value of \( AD \) will be:
Heights of two similar triangles are 3 cm and 4 cm respectively. Ratio of the areas of the triangles will be:
Areas of two similar triangles are in the ratio $16 : 25$. The ratio of corresponding sides of the triangles will be:
In \( \triangle ABC \) if \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm, and \( BC = 6 \) cm, then measure of \( \angle B \) will be:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then prove that the two triangles are similar.