Which statement best explains whether Δ ABC is congruent to Δ DEF? Question 10 options:

ΔABC is not congruent to ΔDEF because there is no sequence of rigid motions that maps ΔABC to ΔDEF.

ΔABC is congruent to ΔDEF because ΔABC can be mapped to ΔDEF by a reflection across the y-axis followed by a translation 5 units down.

ΔABC is congruent to ΔDEF because ΔABC can be mapped to ΔDEF by a translation 5 units down followed by a reflection across the x-axis.

ΔABC is congruent to ΔDEF because ΔABC can be mapped to ΔDEF by a translation 5 units down.

is congruent to because can be mapped to by a reflection across the -axis followed by a translation units down.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4