Question

Prove:

ΔDEF is equilateral, m∠D=x+y, m∠E=2x-y.

Answer 1

To prove that Triangle DEF is equilateral, we need to show that all three angles are equal and all three sides are equal in length. Given the given information, we set up two equations and solve for the values of x and y that satisfy both equations.

Step-by-step explanation:

To prove that Triangle DEF is equilateral, we need to show that all three angles are equal and all three sides are equal in length.

Given that m∠D = x + y and m∠E = 2x - y, we can set up two equations and solve for x and y:

1. x + y = 60 (since angles in an equilateral triangle are all 60 degrees)
2. 2x - y = 60

Solving these equations will give us the values of x and y that satisfy both equations. With x = 30 and y = 30, we can conclude that Triangle DEF is equilateral because all angles are equal and all sides are equal in length.