# Unit 5 relationships in triangles homework 1 triangle midsegments

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## Question:

Unit 5 relationships in triangles homework 1 triangle midsegments 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).
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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

2. The segment parallel to the given segments are:

a.) YZ║RT

3. Given:

FG = 37; KL = 48; GH = 30

a.) FH = ½(KL)

• Substitute

FH = ½(48)

FH = 24

b.) JL = 2(FG)

• Substitute

JL = 2(37)

JL = 74

c.) KJ = 2(GH)

• Substitute

KJ = 2(30)

KJ = 60

d.) FJ = ½(KJ)

• Substitute

FJ = ½(60)

FJ = 30

4. Given:

PT = 13

EN = 43

CP = 29

a.) AE = 2(PT)

• Substitute

AE = 2(13)

AE = 26

b.) AN = 2(CP)

• Substitute

AN = 2(29)

AN = 58

c.) CT = ½(EN)

• Substitute

CT = ½(43)

CT = 21.5

d.) Perimeter of ΔAEN = EN + AN + AE

• Substitute

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