The Hypotenuse Angle Theorem, similar to the HL Theorem, states that if the hypotenuse and one angle of a right triangle are congruent to the hypotenuse and corresponding angle of another right triangle then the triangles are congruent. Prove the HA theorem

Step-by-step explanation:

In order to proof the HA theorem, we consider two triangles  and   which are right angle triangles. The right angle lies at points  and   respectively.

We also consider that the hypotenuse are congruent meaning  and  .

Now we have taken that angle  and  .

Since  and  are 90 degrees, so angle B would be congruent to angle E i.e  

Hence by Angle, side and angle congruence in both triangles we can write as,  .

And this is what the HA thoerem states also

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: