Two chords are congruent if and only if the associated central angles are congruent. true or false.

True

In geometry, a chord is any line segment that join two points on a circle while a central angle a central angle is an angle between two radii in a circle. Two chords are congruent if they measure the same length and this occur if and only if the associated Central angles are congruent. To understand this, focus on the figures below. The lines in red are chords and A and B are central angles. The chords will be congruent if and only if the associated Central angles are congruent, that is, A = B.

True, two chords are congruent if and only if the associated central angles are congruent.

A chord is a segment in which both endpoints lie on the circle.  One of the chord theorems states that two chords are congruent if and only if they are equidistant from the center.  This means that the radii (plural for radius) formed from each endpoint to the center will be congruent.

Each radius forms two sides of a triangle with each chord.  This means we have three sides of each triangle congruent; by the Side-Side-Side theorem, this means that both triangles are congruent.  Since the triangles are congruent, the corresponding angles in each triangle are congruent; this means that the central angles are congruent.

Learn more about congruent chords:  

Learn more about central angles:  link

Keywords:  Congruent chords, congruent central angles, chords of a circle

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step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!