Match each set of conditions with the corresponding relationship between aabc and axyz and the criterion (if any) that proves the relationship.
ab = xy, bc = yz, and angle b
is congruent to angle y.
aabc and axyz are congruent by
the sss criterion
ab = xy, and angles a and b are
congruent to angles x and y
respectively
aabc and axyz are not
necessarily congruent.
angles a, b, and care congruent
to angles x, y, and z, respectively
aabc and axyz are congruent by
the sas criterion
ab = xy, bc = yz, and ca = zx
aabc and axyz are congruent by
the asa criterion.

Step-by-step explanation:

1)AB = XY, BC = YZ, and angle B  is congruent to angle Y

 ΔABC and ΔXYZ are congruent by  the SAS criterion

2)AB = XY; angles A and B are  congruent to angles X and Y  respectively.

ΔABC and ΔXYZ are congruent by  the ASA criterion.

3) AB = XY, BC = YZ, and CA = ZX

ΔABC and ΔXYZ are congruent by  the SSS criterion.

4)Angles A, B, and Care congruent  to angles X, Y, and Z, respectively.

ΔABC and ΔXYZ are not necessarily congruent.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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