Explanation:
Given
E, F, G and H are the mid-points of the sides of a parallelogram ABCD respectively.
To Prove
ar (EFGH) = ½ ar(ABCD)
Construction
Let us join HF.
Proof
In parallelogram ABCD,
AD = BC and AD || BC (Opposite sides of a parallelogram are equal and parallel)
AB = CD (Opposite sides of a parallelogram are equal)
1/2 AD = 1/2 BC
AH = BF and AH || BF ( H and F are the mid-points of AD and BC)
Therefore, ABFH is a parallelogram.
Since ΔHEF and parallelogram ABFH are on the same base HF and between the same parallel lines AB and HF,
∴
∴ ar (EFGH) = ½ ar(ABCD)
hanji afcourse
pusho
[tex]\huge {\green {\sf {\underline {\underline {Answer}}}:-}}[/tex]
Given, The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13.
To find, All the angles of the quadrilateral.
The sum of interior angles in a quadrilateral is 360 degrees.
Let the angles of the quadrilateral be 3x, 5x, 9x, and 13x respectively.
The sum of all interior angles of a quadrilateral is 360°.
[tex]3x + 5x + 9x + 13x = 360° \\ →30x = 360° \\ x = 12° \\ Hence, \: the \: angles \: are
\\ 3x = 3 × 12 = 36° \\ 5x = 5 × 12 = 60° \\ 9x = 9 × 12 = 108° \\ 13x = 13 × 12 = 156°[/tex]
[tex]\huge\dag\sf\red{By \: Divyanshu}[/tex]
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
Explanation:
Given
E, F, G and H are the mid-points of the sides of a parallelogram ABCD respectively.
To Prove
ar (EFGH) = ½ ar(ABCD)
Construction
Let us join HF.
Proof
In parallelogram ABCD,
AD = BC and AD || BC (Opposite sides of a parallelogram are equal and parallel)
AB = CD (Opposite sides of a parallelogram are equal)
1/2 AD = 1/2 BC
AH = BF and AH || BF ( H and F are the mid-points of AD and BC)
Therefore, ABFH is a parallelogram.
Since ΔHEF and parallelogram ABFH are on the same base HF and between the same parallel lines AB and HF,
∴
∴ ar (EFGH) = ½ ar(ABCD)
hanji afcourse
pusho
[tex]\huge {\green {\sf {\underline {\underline {Answer}}}:-}}[/tex]
Given, The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13.
To find, All the angles of the quadrilateral.
The sum of interior angles in a quadrilateral is 360 degrees.
Let the angles of the quadrilateral be 3x, 5x, 9x, and 13x respectively.
The sum of all interior angles of a quadrilateral is 360°.
[tex]3x + 5x + 9x + 13x = 360° \\ →30x = 360° \\ x = 12° \\ Hence, \: the \: angles \: are
\\ 3x = 3 × 12 = 36° \\ 5x = 5 × 12 = 60° \\ 9x = 9 × 12 = 108° \\ 13x = 13 × 12 = 156°[/tex]
[tex]\huge\dag\sf\red{By \: Divyanshu}[/tex]