List of top Mathematics Questions on Triangles

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 given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
In the given figure, DE \(\parallel\) BC. If \(\frac{AD}{DB} = \frac{1}{3}\) and AC = 6 cm, then length AE is
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.
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, DE \(\parallel\) AC and DF \(\parallel\) AE. Prove that : \(\frac{BF}{FE} = \frac{BE}{EC}\).
In the given figure, \(DE \parallel BC\). If \(\frac{AD}{DB} = \frac{1}{3}\) and \(AC = 6\) cm, then length AE is
If in a \(\Delta ABC\), \(AB = 6\) cm and \(DE \parallel BC\) such that \(AE = \frac{1}{3} AC\), then the length of BD is
ABCD is a trapezium in which AB || DC and E, F are points on AD and BC respectively such that EF || DC. If ED = 36 cm, BF = 70 cm and FC = 30 cm, then the length of AD is :
In a triangle \(ABC\), if \[ a=2,\qquad b=4,\qquad \cos C=-\frac{5}{16}, \] then the circumradius \(R\) is
In \(\triangle ABC\), if \[ c=9,\qquad s=10,\qquad \Delta=10\sqrt2, \] then \[ \sin\frac{C}{2} = \]
In \(\Delta\) ABC, AD is a median. X is a point on AD such that AX : XD = 2 : 3. BX is extended so that it intersects AC at Y. Prove that BX = 4 XY.
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
Assertion (A) : tan 2\(\theta\) is not defined at \(\theta\) = 45\(^{\circ}\).
Reason (R) : sin 90\(^{\circ}\) \(\neq\) cos 90\(^{\circ}\).
In the given figure, \(\Delta ABE \cong \Delta ACD\). Prove that \(\Delta ADE \sim \Delta ABC\).
In the given figure, \(OA \times OB = OC \times OD\). Which of the following option is correct ?
In \(\Delta ABC\), AD is a median. X is a point on AD such that AX : XD = 2 : 3. BX is extended so that it intersects AC at Y. Prove that BX = 4 XY.
Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ. If PR and QS intersect at T, prove that ST \(\times\) TQ = PT \(\times\) TR.

In $\Delta ABC$, AD is a median. X is a point on AD such that $AX : XD = 2 : 3$. BX is extended so that it intersects AC at Y. Prove that $BX = 4 XY$.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\frac{AO}{OC} = \frac{BO}{OD}$. Show that quadrilateral ABCD is a trapezium.
Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
S is any point on the side QR of a \(\Delta PQR\) such that \(\angle PSR = \angle QPR\). Prove that \(\frac{QR}{RP} = \frac{RP}{RS}\).
In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC.

35(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)
In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC.

34(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)
In the given figure, \(\triangle\)ABC is right angled triangle with \(\angle\)A = \(90^\circ\). AD is perpendicular to BC.

(a)(i) Prove that \(\triangle\)DBA \(\sim\) \(\triangle\)DAC
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 \( AC \).