Midsegment of a Triangle Worksheets - Math Monks - Free Printable

This worksheet is about the Midsegment Theorem of a Triangle, which states:

> The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length.

We’ll apply this theorem to each problem.

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Problem 1

Triangle ACD, with BE as the midsegment.

- B is midpoint of AC (marked with single tick).
- E is midpoint of AD (marked with single tick).
- So, BE is the midsegment → BE = ½ CD

Given: BE = 4
So, CD = 2 × BE = 8

✔ Answer: CD = 8

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Problem 2

Triangle TPQ, with RS as the midsegment.

- R is midpoint of TP (single tick marks on TR and RP).
- S is midpoint of TQ (single tick marks on TS and SQ).
- So, RS is midsegment → RS = ½ PQ

Given: RS = 6
So, PQ = 2 × RS = 12

✔ Answer: PQ = 12

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Problem 3

Triangle JLM, with KN as the midsegment.

- K is midpoint of JL (double tick marks on JK and KL).
- N is midpoint of JM (single tick marks on JN and NM).
- So, KN is midsegment → KN = ½ LM

Given: LM = 30
So, KN = ½ × 30 = 15

✔ Answer: NK = 15

*(Note: NK is same as KN)*

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Problem 4

Triangle EFI, with GH as the midsegment.

- G is midpoint of EI (single tick marks on EG and GI).
- H is midpoint of FI (double tick marks on FH and HI).
- So, GH is midsegment → GH = ½ EF

Given: EF = 18
So, GH = ½ × 18 = 9

✔ Answer: GH = 9

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Problem 5

Triangle MOP, with QN as the midsegment.

- Q is midpoint of MP (double tick marks on MQ and QP).
- N is midpoint of MO (single tick marks on MN and NO).
- So, QN is midsegment → QN = ½ OP

Given: QN = 12
So, OP = 2 × 12 = 24

But the question asks for PO, which is same as OP → 24

Also given: PO = x + 21
So, set up equation:
x + 21 = 24
→ x = 3

✔ Answer: PO = 24

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Problem 6

Triangle SVW, with TU as the midsegment.

- T is midpoint of SV (single tick marks on ST and TV).
- U is midpoint of SW (single tick marks on SU and UW).
- So, TU is midsegment → TU = ½ VW

Given:
- TU = x + 4
- VW = x + 10

Apply midsegment theorem:
TU = ½ VW
→ x + 4 = ½ (x + 10)

Solve for x:

Multiply both sides by 2:
2(x + 4) = x + 10
2x + 8 = x + 10
2x - x = 10 - 8
x = 2

Now plug back in:

- TU = x + 4 = 2 + 4 = 6
- VW = x + 10 = 2 + 10 = 12

✔ Answers: TU = 6, VW = 12

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## ✔ Final Answers:

1. CD = 8
2. PQ = 12
3. NK = 15
4. GH = 9
5. PO = 24
6. TU = 6, VW = 12

Let me know if you’d like a diagram explanation or step-by-step drawing!