Answer:
Part A) see the explanation
Part B) see the explanation
Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters
Step-by-step explanation:
<u><em>The complete question is</em></u>
The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC
Part A) Write a similarity statement for each of the four pair of corresponding sides
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
The corresponding sides are
AB and EF
BC and FG
CD and GH
AD and EH
so
Part B) Write a congruence statement for each of the four pair of corresponding angles.
we know that
If two figures are similar, then its corresponding angles are congruent
The corresponding angles are
∠A and ∠E
∠B and ∠F
∠C and ∠G
∠D and ∠H
so
∠A ≅ ∠E
∠B ≅ ∠F
∠C ≅ ∠G
∠D ≅ ∠H
Part C) Determine the perimeter for each of the isosceles trapezoids
we have
The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC
step 1
Find the measure of CD
Remember that
The ratio between corresponding sides is proportional and this ratio is the scale factor
Let
z ----> the scale factor
so
we have
substitute
step 2
Find the measure of AB
Remember that
AB is three times the length of DC
so
substitute
step 3
Find the measure of BC
Remember that in an isosceles trapezoid, the legs are equal
so
BC=AD
we have
therefore
step 4
Find the perimeter of trapezoid ABCD
substitute the values
step 5
Find the perimeter of trapezoid EFGH
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z ---> the scale factor
x ----> the perimeter of trapezoid ABCD
y ----> the perimeter of trapezoid EFGH
so
we have
substitute
therefore
The perimeter of trapezoid EFGH is 48 centimeters