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Which lines are parallel? Justify your answer.
р
9
130°
1300
O Lines p and q are parallel because same side
interior angles are congruent.
O Lines p and q are parallel because alternate
exterior angles are congruent
O Lines land m are parallel because same side
interior angles are supplementary
O Lines land m are parallel because alternate interior
angles are supplementary.
m
80°

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3

it is rigid.; it is isometric. ; the size is preserved.

step-by-step explanation:

a translation is called an isometry; these are transformations that preserve congruence between pre-images and images.

they are also called rigid transformations, as the only thing that can happen to a pre-image is that it is moved or turned, not stretched or shrunk.

since congruence is preserved, the size is preserved.