Answer:
C
Step-by-step explanation:
To determine the ratio, we need to know the formula of the area of an hexagon in terms of the length of its sides. We cannot directly conclude that the ratio would be 3, the same as that of the ratio of the lengths of the side, since it may be that the relationship of the area and length is not equal. The area of a hexagon is calculated by the expression:
A = (3√3/2) a^2
So, we let a1 be the length of the original hexagon and a2 be the length of the new hexagon.
A2/A1 = (3√3/2) a2^2 / (3√3/2) a1^2
A2/A1 = (a2 / a1)^2 = 3^2 = 9
Therefore, the ratio of the areas of the new and old hexagon would be 9.
Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:
1. a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. a.) FH = 24
b.) JL = 74
c.) KJ = 60
d.) FJ = 30
4. a.) AE = 26
b.) AN = 58
c.) CT = 21.5
d.) Perimeter of ΔAEN = 127
5. x = 15
6. x = 6
<h3>What are Parallel lines?</h3>
Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.
<h3>The Triangle Midsegment Theorem</h3>
- A midsegment is a line that connects the midpoints of the two sides of a triangle together.
- Every triangle three midsegments.
- Based on the Midsegment Theorem of a triangle, the third side of a triangle is always parallel to the midsegment, and thus, the third side is twice the size of the midsegment. In order words, length of midsegment = ½(length of third side).
Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:
1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:
a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. The segment parallel to the given segments are:
a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. Given:
FG = 37; KL = 48; GH = 30
a.) FH = ½(KL)
FH = ½(48)
FH = 24
b.) JL = 2(FG)
JL = 2(37)
JL = 74
c.) KJ = 2(GH)
KJ = 2(30)
KJ = 60
d.) FJ = ½(KJ)
FJ = ½(60)
FJ = 30
4. Given:
PT = 13
EN = 43
CP = 29
a.) AE = 2(PT)
AE = 2(13)
AE = 26
b.) AN = 2(CP)
AN = 2(29)
AN = 58
c.) CT = ½(EN)
CT = ½(43)
CT = 21.5
d.) Perimeter of ΔAEN = EN + AN + AE
Perimeter of ΔAEN = 43 + 58 + 26
Perimeter of ΔAEN = 127
5. 10x + 44 = 2(8x - 23) (midsegment theorem)
10x + 44 = 16x - 46
10x - 16x = -44 - 46
-6x = -90
Divide both sides by -6
x = 15
6. 19x - 28 = 2(6x + 7) (midsegment theorem)
19x - 28 = 12x + 14
19x - 12x = 28 + 14
7x = 42
x = 6
Learn more about midsegment theorem on:
brainly.com/question/11482568