SOLUTION: Igcse math pythagoras theorem worksheet - Studypool - Free Printable

Let's solve each question step by step, based on the Pythagoras Theorem worksheet. We'll identify the hypotenuse in right-angled triangles and complete the statements.

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QUESTION 1: Name the hypotenuse of each right-angled triangle

In a right-angled triangle, the hypotenuse is the side opposite the right angle, and it is the longest side.

#### a) Triangle ABC
- Right angle at C
- So, hypotenuse is the side opposite to ∠C → AB
- Side AB is labeled as c
✔ Answer: c (or AB)

#### b) Triangle PQR
- Right angle at R
- Hypotenuse is opposite to ∠R → PQ
- PQ is labeled as r
✔ Answer: r (or PQ)

#### c) Triangle LMN
- Right angle at N
- Hypotenuse is opposite to ∠N → LM
- LM is labeled as n
✔ Answer: n (or LM)

#### d) Triangle RTS
- Right angle at T
- Hypotenuse is opposite to ∠T → RS
✔ Answer: RS

#### e) Triangle UWV
- Right angle at W
- Hypotenuse is opposite to ∠W → UV
✔ Answer: UV

#### f) Triangle KJL
- Right angle at L
- Hypotenuse is opposite to ∠L → KJ
✔ Answer: KJ

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✔ Answers for Question 1:

a) c or AB
b) r or PQ
c) n or LM
d) RS
e) UV
f) KJ

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QUESTION 2: Name the hypotenuse of the triangle named below the diagram

We need to identify the hypotenuse of the specific triangle mentioned.

#### a) △ADC
- Look at square ABCD with diagonals intersecting at E
- Triangle ADC has vertices A, D, C
- Angles at A and C are not right angles; but angle at D is 90° (since ABCD is a square)
- So, right angle at D → hypotenuse is AC
✔ Answer: AC

#### b) △PSR
- Rectangle PSRQ with diagonals crossing at T
- Triangle PSR: points P, S, R
- Angle at S is 90° (rectangle corner)
- So, right angle at S → hypotenuse is PR
✔ Answer: PR

#### c) △LJM
- Rhombus or parallelogram with diagonals intersecting at J
- Triangle LJM: vertices L, J, M
- Diagonals intersect at right angles? Yes — shown by small square at J
- So, angle at J is 90° → right angle at J
- Hypotenuse is opposite to ∠J → LM
✔ Answer: LM

#### d) △PST
- Points P, S, T
- Right angle at S (marked with square)
- So, hypotenuse is PT
✔ Answer: PT

#### e) △CBD
- Triangle CBD: C, B, D
- Right angle at B (marked)
- So, hypotenuse is CD
✔ Answer: CD

#### f) △FHG
- Triangle FHG: F, H, G
- Right angle at H (marked)
- So, hypotenuse is FG
✔ Answer: FG

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✔ Answers for Question 2:

a) AC
b) PR
c) LM
d) PT
e) CD
f) FG

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QUESTION 3: Complete the following statements

Given triangle DEF, with right angle at F (since the right angle symbol is at F), and sides:
- EF = d
- FD = e
- DE = f

So:
- Side opposite to ∠D → EF = d
- Side opposite to ∠E → FD = e
- Side opposite to ∠F → DE = f ← this is the hypotenuse

Now:

#### a) ________ is the length of the side opposite to angle D.
→ Opposite to ∠D is EF, which is d
✔ Answer: d

#### b) ________ is the length of the side opposite to angle E.
→ Opposite to ∠E is FD, which is e
✔ Answer: e

#### c) ________ is the length of the side opposite to angle F.
→ Opposite to ∠F is DE, which is f
✔ Answer: f

#### d) ________ is the length of the hypotenuse of △DEF.
→ Hypotenuse is DE = f
✔ Answer: f

#### e) ________ is the area of the square on the side opposite to ∠D.
- Side opposite to ∠D is EF = d
- Area of square on that side = d²
✔ Answer: d²

#### f) ________ is the area of the square on the side opposite to ∠F.
- Side opposite to ∠F is DE = f
- This is the hypotenuse
- Area of square on hypotenuse = f²
✔ Answer: f²

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✔ Answers for Question 3:

a) d
b) e
c) f
d) f
e) d²
f) f²

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✔ Final Summary:

#### Question 1:
a) c
b) r
c) n
d) RS
e) UV
f) KJ

#### Question 2:
a) AC
b) PR
c) LM
d) PT
e) CD
f) FG

#### Question 3:
a) d
b) e
c) f
d) f
e) d²
f) f²

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