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
What are Parallel lines?
Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.
The Triangle Midsegment Theorem
- 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:
https://brainly.com/question/11482568
