Students were asked to answer a question at education and to express what is most important for them to succeed. The one that response stood out from the rest was practice. Persons who are definitely successful do not become successful by being born. They work hard and commitment their lives to succeeding. If you want to get your goals, keep this in mind! shown below some question and answer examples that you would certainly make use of to expand your knowledge and gain insight that will assist you to maintain your school studies.

## Question:

Unit 5 relationships in triangles homework 1 triangle midsegments

## Answer:

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

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

- Add like terms together

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

- Add like terms together

19x – 12x = 28 + 14

7x = 42

- Divide both sides by 7

**x = 6**

Learn more about **midsegment theorem** on:

They could actually hopefully assist the student sort out the question by obtaining the questions and answer examples. You could then have a discussion with your classmate and continue the school learning by studying the question alogside each other.