Given:In \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{DEF}, \mathrm{AB}=\mathrm{DE}, \mathrm{AB} \| \mathrm{DE}, \mathrm{BC}=\mathrm{EF} \) and \( \mathrm{BC} \| EF \).To do :We have to show that(i) quadrilateral ABED is a parallelogram(ii) quadrilateral \( \mathrm{BEFC} \) is a parallelogram(iii) \( \mathrm{AD} \| \mathrm{CF} \) and \( \mathrm{AD}=\mathrm{CF} \)(iv) quadrilateral ACFD ... Read More

Given:$ABCD$ is a rectangle in which diagonal $AC$ bisects $\angle A$ as well as $\angle C$.To do :We have to show that(i) $ABCD$ is a square(ii) Diagonal $BD$ bisects $\angle B$ as well as $\angle D$. Solution :(i) A square is a rectangle when all sides are equal. In the above figure, ... Read More

Given:In parallelogram \( \mathrm{ABCD} \), two points \( \mathrm{P} \) and \( \mathrm{Q} \) are taken on diagonal \( \mathrm{BD} \) such that \( \mathrm{DP}=\mathrm{BQ} \)To do :We have to show that (i) \( \triangle \mathrm{APD} \equiv \triangle \mathrm{CQB} \)(ii) \( \mathrm{AP}=\mathrm{CQ} \)(iii) \( \triangle \mathrm{AQB} \equiv \triangle \mathrm{CPD} \)(iv) ... Read More

Given:\( \mathrm{ABCD} \) is a rhombus.To do :We have to show that diagonal \( \mathrm{AC} \) bisects \( \angle \mathrm{A} \) as well as \( \angle \mathrm{C} \) and diagonal \( \mathrm{BD} \) bisects \( \angle \mathrm{B} \) as well as \( \angle \mathrm{D} \).Solution :  $AC$ and $BD$ are the ... Read More

Given:The mass of object A is 6kg whereas that of another object B is 34 kg. To do:We have to find the object that has more inertia.Solution:We know that, Inertia is directly proportional to the mass of the body. The more the mass, the more inertia.Here, object B which is 34 kg is ... Read More

Given :Diagonals of the quadrilateral bisect each other at right angles.To do :We have to show that it is a rhombus.Solution:                              Let $ABCD$ be a quadrilateral in which diagonals bisect each other at right angles.So, $OA=OC, OB=OD$$\angle ... Read More

Given :Diagonals of the quadrilateral are equal and bisect each other at right angles.To do :We have to show that it is square.Solution :                              Let $ABCD$ be a quadrilateral in which diagonals are equal and bisect each ... Read More

Given:In right triangle $ABC$, right angled at $C$, $M$ is the mid-point of hypotenuse $AB$. $C$ is joined to $M$ and produced to a point $D$ such that  $DM=CM$. Point $D$ is joined to point $B$.To do:We have to show the given questions.Solution:(i) Let us consider $\triangle AMC$ and $\triangle ... Read More

Given:In an isosceles triangle  $ABC$, with $AB=A$, the bisectors of $\angle B$ and $\angle C$ intersect each other at $O$. Join $A$ to $O$.To do:We have to show that(i) $OB=OC$(ii) $AO$ bisects $\angle A$.Solution:(i) We know that, In an isosceles triangle all the angle are equal.This implies, $\angle B= \angle ... Read More

Given:In $\triangle ABC, AD$ is the perpendicular bisector of $BC$.To do:We have to show that $\triangle ABC$ is an isosceles triangle in which  $AB=AC$.Solution:Let us consider $\triangle ADB$ and$\triangle ADC$, We know that, According to Rule of Side-Angle-Side Congruence:Triangles are said to be congruent if any pair of corresponding sides ... Read More