Fill in the missing statement and reason in the proof of the Alternate Interior Angles Theorem. It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem. ∠EGB and ∠EHD are congruent according to the _. Finally, _ by the Transitive Property of Equality.

Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent

Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent

Corresponding Angles Theorem; ∠EGB and ∠EHD are congruent

Alternate Exterior Angles Theorem; ∠AGF and ∠EHD are congruent

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!