### Theorems related to triangles - class-X

Description: theorems related to triangles | |

Number of Questions: 37 | |

Created by: Sara Dalvi | |

Tags: geometry maths pythagoras theorem |

Find the side of the square whose diagonal is $16 \sqrt 2$ cm.

The sides of triangle are in A.P. and the greatest angle exceeds the least by 90. The sides are in the ratio _____________.

If H is orthocenter of triangle PQR then PH + QH + RH is

ABC is a triangle right angle at B. D is a point on AC such that $\angle ABD = 45^0$. If AC =$6$ and AD =$2$ , then AB is

consider a triangle PQR in which the relation $ QR^2+PR^2=5*PQ^2$ holds. let G be the point of intersection of the medians PM and QN . then angle QGM is always

If in a $\Delta ABC,\sin A=\sin^{2} B$ and $2\cos^{2}A=3\cos^{2}B$, then the $\Delta ABC$ is

Which of the following can be the sides of a right-angled triangle?

Let $\Delta _1$ denotes the area of the triangle formed by the vertices $(a^3m^3 _1, am _1), (a^3m^3 _2am _2), (a^3m^3 _3, am _3)$ and $\Delta _2$ denotes the area of the triangle formed by the vertices $(2am _1m _2, a^2(m^2 _1+m^2 _2))$, $(2am _2m _3, a^2(m^2 _2+m^2 _3))$ and $(2am _3m _1, a^2(m^2 _3+m^2 _1))$. Then $\dfrac{\Delta _1}{\Delta _2}(a > 0)$ equals?

The sides of $\Delta ABC$ are 5, 7, 8 units then $AG^2 + BG^2 + CG^2$ where G is centroid of $\Delta ABC$ is

For a right-angled triangle, two small sides are of $6$cm and $8$cm length. Length of third side will be

In $\Delta ABC, \, m \angle B = 90$ and $\overline{BM}$ is an altitude. If AB = 2 AM, then AC = ......

P, Q, R are the points of intersection of a line 1 with sides BC, CA, AB of a $\Delta$ ABC

respectively, then $\dfrac{BP}{PC} \dfrac{CQ}{QA} \dfrac{AR}{RB}$

Sides of triangle are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

The hypotenuse and the semi-perimeter of right triangle are 20 cm and 24 cm, respectively. The other two sides of the triangle are :

In $\Delta PQR,\angle P$ is right angle and $\bar{PM}$ is an altitude. $PQ=\sqrt{20}$ and QM=4 then RM=____.

The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle:

The length of the hypotenuse of an isosceles right triangle whose one side is $4\surd {2}\ cm$ is___________$cm$

Let $ABC$ be a fixed triangle and $P$ be variable point in the plane of a triangle $ABC$. Suppose $a, b, c$ are lengths of sides $BC, CA,AB$ opposite to angles $A, B, C $ respectively. If $a(PA)^{2} + b(PB)^{2} + c(PC)^{2}$ is minimum, then the point $P$ with respect to $\triangle{ABC}$ is

If $AD,BE$ and $CF$ are the medians of a $\Delta ABC,$ then evaluate $\displaystyle \left ( AD^{2}+BE^{2}+CF^{2} \right ):\left ( BC^{2}+CA^{2}+AB^{2} \right )=$

The distances of the circumcentre of the acute-angled $ \Delta \mathrm{ABC} $ from the sides $ \mathrm{BC}, $ CA and AB are in the ratio

Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle, then $S\vec { A } +S\vec { B } +S\vec { C } =$

Mark the correct alternative of the following.

In a right triangle, one of the acute angles is four times the other. Its measure is?

Find the perimeter of an isosceles right triangle with each of its congruent as 7cm.

If the sides of a triangle are in the ratio $1\, :\, \sqrt2\, :\, 1$, then the triangle is:

In $\triangle ABC$, AP is the median. If $AP=7$ and $AB^2+AC^2=260$, then find BC.

Find the length of median. If the sides of triangle are:

$a = 5, b = 6, c = 8$. and $m = 3, n = 2$.

In a $\Delta$ $ABC, AD = 3, BC = 2, AB = 1$, find the value of $AC$. (Use Apollonius theorem).

In a $\Delta$ $ABC, AC = 6, BC = 2, AB = 4$, find the value of $AD$. (Use Apollonius theorem).

In a $\Delta$ $ABC, AC = 8, BC = 2, AB = 6$, find the value of $AD$. (Use Apollonius theorem).

In a $\Delta$ $ABC, AC = 4, BC = 2, AB = 6$, find the value of $AD$. (Use Apollonius theorem).

In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side is called ______ theorem.

In a $\Delta$ $ABC, AC = 6, BC = 2, AB = 8$, find the value of $AD$. (Use Apollonius theorem).

Which one of the following formula is used to find apollinius theorem for isosceles triangle?

In a $\triangle ABC$, $AB= 4$ cm and $AC = 8$ cm. If M is the midpoint of BC and $AM = 3$ cm, then the length of $BC$ in cm is:

In $\triangle PQR$, $\angle P=30^o$, $\angle Q=60^0$, $\angle R= 90^o$ and $PQ=10 $ units.

According to Apolloneous Theorem, if $\overline AD$ is a median of $\triangle ABC$, then $AB^{2}+AC^{2}=$