Whose sequence proves triangle ABC is congruent to triangle DEF? Why?

5b. y = −2

5a. y = 3

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

Step-by-step explanation:

5.

b. y = −2

a. y = 3

* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], but in this case, since the slope is undefined [5b], we just take the y-coordinate of the ordered pair.

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES], but in this case, since the slope is zero [5a], we just take the y-coordinate of the ordered pair.

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

* 1¾ = 7⁄4

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES].

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