How to work this out? in a circle with an 8-inch radius, a central angle has a measure of 60°. how long is the segment joining the endpoints of the arc cut off by the angle?

The length of segment joining the endpoints of the arc is

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

-----> is the radius of the circle  

----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to

The equilateral triangle has three equal sides and tree equal angles

so

Hence

The length of segment joining the endpoints of the arc is

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.