Question

list all pairs of congruent angles and write the ratios of the corresponding lengths in a statement of proportionality. given ABCD ~ EFGH

Answer 1

Corresponding lengths and congruent angles

Initial explanation

We have two rectangles, the rectangle of the length is transformed to the rectangle of the right.

Both rectangles are similar, this is, they have the same form but different size. We can see it clearly if we rotate the second rectangle:

Congruent angles

Since all the angles are right angles, all the angles are congruent:

∠A ≅ ∠B ≅ ∠C ≅ ∠D ≅ ∠E ≅ ∠F ≅ ∠G ≅ ∠H

The pairs corresponding angles are between rectangles are:

∠A ≅ ∠G

∠B ≅ ∠H

∠C ≅ ∠F

∠D ≅ ∠E

Constant of proportionality

Now, we can write the corresponding sides

AB ⇄ GH

CD ⇄ FE

AC ⇄ GF

BD ⇄ HE

If we divide each pair of corresponding lengths, we will obtain the same result:

`(AB)/(GH)=(CD)/(FE)=(AC)/(GF)=(BD)/(HE)`

Let's calculate any of those divisions:

`(CD)/(FE)=(12)/(9)=(4)/(3)`

Then, the constant of proportionality is 4/3

`(AB)/(GH)=(CD)/(FE)=(AC)/(GF)=(BD)/(HE)=(4)/(3)`