Question

In: Math

1 (a) Given Δ ABC , construct equilateral triangles Δ BCD , Δ CAE , and...

1

(a) Given Δ ABC , construct equilateral triangles Δ BCD , Δ CAE , and Δ ABF outside of Δ ABC . Prove that AD = BE=CF .

(b)Let ABCD be a convex quadrilateral. Show that the sum of the two diagonals of ABCD is less than the perimeter P of ABCD, but more than the semiperimeter P 2 of ABCD.

Expert Solution

(a)

Here it is given Δ BCD , Δ CAE , and Δ ABF are equilateral.

We have to prove AD = BE=CF

Hence proved

(b)

Given ABCD is a convex quadrilateral.

That is all the inside angles are less than 180.

We have to prove that the sum of the two diagonals of ABCD is less than the perimeter P of ABCD, but more than the semiperimeter P2 of ABCD.

Hence we have proved that the sum of the two diagonals of ABCD is less than the perimeter of ABCD

Hence we have proved that sum of the two diagonals of ABCD is greater than the semiperimeter of ABCD.

milcah answered 2 years ago

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