the vertices of δghi are g (2, 4), h (4, 8), and i (8, 4). the vertices of δjkl are j (1, 1), k (2, 3), and l (4, 1). which conclusion is true about the triangles?
a. they are congruent by the definition of congruence in terms of rigid motions.
b. they are similar by the definition of similarity in terms of a dilation.
c. the ratio of their corresponding sides is 1: 3
d. the ratio of their corresponding angles is 1: 3.

b. they are similar by the definition of similarity in terms of a dilation.

step-by-step explanation:

when you graph them, it's easier to visualize what's going on. you can use distance formula to determine a ratio. line gh and line jk are similar. the same goes for each of the corresponding side lengths. when all the side lengths are the similar, you can conclude that all of the angles must also be the same. a triangle that is 3 in x 3 in x 3 in has the same angle measures as a triangle that is 3 ft x 3 ft x 3 ft, even though the side lengths have changed size. they are still proportionate.

when the ratios of both corresponding sides and corresponding angles are the same, the triangles are similar.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!