Question

Please help and show work thank you.

Answer 1

An equilateral triangles has 3 equal sides and 3 equal angles.
All the angles of an equilateral triangle have a measure of 60 degrees.

Using the Pythagorean theorem, the length of the hypotenuse squared is the length of one leg squared plus the length of another leg squared.

Here's the equation for the Pythagorean theorem.
Let c be the length of the hypotenuse.
Let a and b be the length of the two legs.
a^2 + b^2 = c^2 

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Answer 2

1.
A triangle has 3 angles. The sum of the measures of the angles in a triangle is always 180 degrees. An equilateral triangle has three angles with the same measure. Since all angles have the same measure and the sum of their measures equals 180 degrees, each angle measures 180/3 = 60 degrees.
Answer: All angles of an equilateral triangle have the same measure, and the measure is 60 degrees.

2.
The Pythagoras theorem tells us that for every right triangle, if the legs have lengths a and b, and the hypotenuse has measure c, then a^2 + b^2 = c. The square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.