Home
Class 7
MATHS
ABCD is quadrilateral. Is AB+BC+CD+DA <...

`ABCD` is quadrilateral. Is `AB+BC+CD+DA < 2(AC+BD) ?`

Text Solution

AI Generated Solution

To prove that \( AB + BC + CD + DA < 2(AC + BD) \) for quadrilateral \( ABCD \), we will use the properties of triangles formed by the diagonals \( AC \) and \( BD \). ### Step-by-Step Solution: 1. **Identify the Quadrilateral and Diagonals**: - Let \( ABCD \) be a quadrilateral with diagonals \( AC \) and \( BD \) intersecting at point \( O \). 2. **Form Triangles**: ...
Promotional Banner

Topper's Solved these Questions

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT ENGLISH|Exercise EXERCISE 6.5|8 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT ENGLISH|Exercise EXERCISE 6.1|1 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|6 Videos

  • SYMMETRY

    NCERT ENGLISH|Exercise EXERCISE 14.2|2 Videos

Similar Questions

Explore conceptually related problems

ABCD is a quadrilateral. Is AB+BC+CD+DA > AC+BD ?

If ABCD is a quadrilateral such that AB = AD and CB = CD , then prove that AC is the perpendicular bisector of BD .

In the adjoining figure, ABCD is a quadrilateral. Its diagonals AC and BD intersect at point 'O'. Prove that : (a) AB+BC+CD+DA lt 2(AC+BD) (b) AB+BC+CD+DA gt (AC+BD)

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects both the angle ABC and angle ADC .

ABCD is a quadrilateral in which AB=AD . The bisector of BAC and CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.

ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and AC respectively. Prove that EFGH is a rhombus.

In the adjoining figure, ABCD is a quadrilateral. M and N are the points on AD and CD respectively such that AB = BC, angleABM=angleCBN and angleMBD=angleNBD . Prove that BM = BN .

ABCD is a quadrilateral in which AB||DC and AD = BC. Prove that angleA=angleB and angleC= angleD .

Show that in a quadrilateral ABCD AB+BC+CD+DA gt AC + BD

Show that in a quadrilateral ABCD AB+BC+CD+DA lt 2 (BD + AC)