Janet is designing a frame for a client. She wants to prove to her client that m∠AGE ≅ m∠CHE in her sketch. What is the missing justification in the proof? Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.

Statement Justification
segment AB is parallel to segment CD with transversal segment EF Given
m∠AGE ≅ m∠HGB Vertical Angles Theorem
m∠HGB ≅ m∠CHE Alternate Interior Angles Theorem
m∠AGE ≅ m∠CHE

A. Alternate Exterior Angles Theorem
B. Corresponding Angles Theorem
C. Reflexive Property
D. Transitive Property

Step-by-step explanation:

false

step-by-step explanation:

the reason i say this is because for a certain length of sides you can pick any two and the length is wither equal or greater than the third side and in this case it's not.

3 + 5 = 8

8 is smaller than 9 which is the third side.

hope this : )

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt