## Angles in a Quadrilateral – GCSE Math

In this chapter we will about about the angles of quadrilateral, also the method to find the missing angle if measure of other angles are given. What are angles in a quadrilateral ? Here we are talking about the interior angles of quadrilateral. It’s the interior angle formed between the two adjacent sides. In Quadrilateral, …

## Sum of exterior angles of quadrilateral

In this post we will first discuss the concept of exterior angles of quadrilateral and then try to find the sum of all the exterior angles. Exterior angles of quadrilateral Exterior angles are formed between one side of quadrilateral and extended side of the other side. Consider the above quadrilateral ABCD.Here ∠1 is the exterior …

In this post we will try to classify quadrilaterals into different shapes and will also mention its associated properties. What are Quadrilateral shape ? Quadrilateral is a 2 dimensional figures with four straight sides. Let us understand the word “Quadrilateral”. Quad means “Four” Lateral means “Sides” Hence, it’s a shape containing four sides. Consider the …

## Properties of Quadrilateral

In this post we will discuss properties and formulas of different quadrilateral in detail. Following quadrilaterals are discussed below; (a) Square(b) Rectangle(c) Parallelogram(d) Rhombus(e) Trapezium Along with the properties, try to remember all the formulas as they would help you solve related questions in examination. Square The square has following properties; (a) All sides are …

## Prove that diagonal of Rhombus are perpendicular

Given:Rhombus is basically a parallelogram with following properties; (a) All sides are equal.i.e. AB = BC = CD = DA (b) Opposite sides are parallel. (c) Diagonals bisect each other.i.e. OA = OC and OD = OB To Prove:Prove that diagonals intersect at right angles.i.e. ∠AOB = 90 degree Proof:Consider triangle AOD and COD; OA …

## Prove that each angle of rectangle measures 90 degree

We know that a rectangle is basically a parallelogram with one angle measures 90 degree. Given:Since all rectangle are form of parallelogram, their opposite sides are parallel.AB || CD and AD || CB. Also one of the angle measures 90 degree.∠A = 90 degree To Prove:Each angle of rectangle measures 90 degree.∠A = ∠B = …

## Prove that if diagonal of quadrilateral bisect each other then it is parallelogram

Consider the below quadrilateral ABCD in which diagonals bisect each other. Given:ABCD is a quadrilateral.AC & BD are diagonals bisecting each other.Hence, AO = OC and BO = OD. To Prove:Prove that the given quadrilateral is a parallelogram. Proof:Consider triangle AOB and COD; AO = OC (given)∠AOB = ∠COD ( vertically opposite angle)BO = OD …

## Prove that diagonals of parallelogram bisect each other

Consider the below parallelogram ABCD with diagonals AC and BD. Given:We know that opposite sides of parallelogram are equal.AB = CDAD = BC Also in parallelogram, opposite sides are parallel to each other.AB || CDAD || BC To prove:Diagonals bisect each other.AO = OCDO = OB Proof:Consider triangle AOD and BOC. AD = BC (given)∠DAO …

## Quadrilateral with equal opposite angle is a parallelogram

In this chapter we will prove that any quadrilateral with equal pair of opposite angles is actually a parallelogram. Consider the quadrilateral ABCD in which opposite angles are equal.∠A = ∠C∠B = ∠D To prove:Prove that ABCD is a parallelogram. Solution:We know that sum of all angles of quadrilateral measure 360 degree. ∠A + ∠B …

## Quadrilateral with equal opposite sides is a parallelogram

In this chapter we will prove that “any quadrilateral with equal opposite sides is actually a parallelogram. Given:Consider quadrilateral ABCD in which opposite sides are equal.AB = CD and AD = BC To Prove:Prove that the quadrilateral is parallelogram.i.e. AB || CD and AD || CB Proof:Consider triangle ABC and CDA; AB = CD ( …

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