f a translation maps ∠I onto ∠K, which of the following statements is true? Triangles HGI and JGK; point H is between points J and G on segment JG, and point I is between points G and K on segment GK. segment HI is twice the measure of segment JK. segment GH is twice the measure of segment GJ. Triangles ΔGHI and ΔGJK are not similar. ∠H ≅ ∠J

The correct option is;

∠H ≅ ∠J

Step-by-step explanation:

Given that a translation maps ∠I onto ∠K, therefore;

in triangles GHI and GJK we have;

∠I ≅ ∠K; Given

∠G = ∠G; Reflexive property

Therefore, ∠H + ∠I + ∠G = 180° (Sum of interior angles in a triangle)

Similarly,  ∠J + ∠K + ∠G = 180° (Sum of interior angles in a triangle)

Which gives;

∠H  = 180° - (∠I + ∠G) = 180° - (∠K + ∠G) = ∠J

Therefore, angle K and angle H are congruent which can be expressed as follows;

∠H ≅ ∠J.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.