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

(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.

Solutions

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 1 year ago

Next > < Previous

Related Solutions

Given Δ ABC , construct equilateral triangles Δ BCD , Δ CAE , and Δ ABF...

Given Δ ABC , construct equilateral triangles Δ BCD , Δ CAE , and Δ ABF outside of Δ ABC . Prove that the circumcircles of Δ BCD , Δ CAE , and Δ ABF are concurrent (go through the same point).

How to calculate the distance between triangles If you have two equilateral triangles and a different...

How to calculate the distance between triangles If you have two equilateral triangles and a different area and one inside the other please simple anwser

If equilateral triangles are constructed on the sides of any triangle, prove that the distances between...

If equilateral triangles are constructed on the sides of any triangle, prove that the distances between the vertices of the original triangle and the opposite vertices of the equilateral triangles are equal.

36) Construct BCD counter and draw block diagram of a three-decade decimal BCD counter. The following...

36) Construct BCD counter and draw block diagram of a three-decade decimal BCD counter. The following must be included (5points) : - a) The truth table of BCD counter b) The implementation of BCD counter c) The three-decades BCD counter

Illustrate in detail how to construct a BCD to 7-segment Decoder.

Given the values of Δ H ∘ rxn , Δ S ∘ rxn , and T...

Given the values of Δ H ∘ rxn , Δ S ∘ rxn , and T below, determine Δ S univ(J/K) (for each part ) . A)ΔH∘rxn= 121 kJ , ΔS∘rxn=− 248 J/K , T= 297 K , B)ΔH∘rxn=− 121 kJ , ΔS∘rxn= 248 J/K , T= 297 K C)ΔH∘rxn=− 121 kJ , ΔS∘rxn=− 248 J/K , T= 297K. D)ΔH∘rxn=− 121 kJ , ΔS∘rxn=− 248 J/K , T= 546 K

Show that of all isosceles triangles with a given perimeter , the one with greatest area...

Show that of all isosceles triangles with a given perimeter , the one with greatest area is equilateral.

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions....

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.) a = 77, b = 104, ∠A = 24° ∠B1 = ° ∠B2 = ° ∠C1 = ° ∠C2 = ° c1 = c2 =

3. Determine ω0, R, and δ so as to write the given expression in the form...

3. Determine ω0, R, and δ so as to write the given expression in the form u=Rcos(ω0t−δ). (a) u= 3 cos(2t) + 4 sin(2t) (b) u=−2 cos(πt)−3 sin(πt)

1. Suppose that for the United States, (%Δ Gun Murder Rate)/(%Δ Gun OwnerShip Rate)= .009 1a....

1. Suppose that for the United States, (%Δ Gun Murder Rate)/(%Δ Gun OwnerShip Rate)= .009 1a. If gun control legislation were able to reduce gun ownership by 99 percent, how exactly would society benefit? 1b. Based upon your answer in 1a, What can you conclude about the likely efficacy of gun control legislation in the United States? 2. Refer back to#1, suppose the demand for guns is QG D = 500 - .45P and the supply of guns is QG...

Subjects