Pythagoras' Theorem

Maths, SSC-KPK Class 9. This chapter is split into 28 topics and has 721 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Sides expressed in x: unknown values (Review Exercise 15 Q5) 30 questions
2. Classifying triangles by sides: acute, right, obtuse 30 questions
3. Theorem 15.2 (converse of Pythagoras' theorem): statement and proof 22 questions
4. Generating and extending Pythagorean triples 30 questions
5. Isosceles triangles and Pythagoras (Review Exercise 15 Q3) 30 questions
6. Finding an unknown leg: surd results 27 questions
7. Right-angled triangle: hypotenuse, legs and notation 20 questions
8. Finding the hypotenuse (whole-number results) (Part 1) 25 questions
9. Theorem 15.1 (Pythagoras' theorem): statement 21 questions
10. Practical distance problems using Pythagoras' theorem 27 questions
11. Verifying a right-angled triangle with the converse 30 questions
12. Finding an unknown leg (whole-number results) (Part 1) 25 questions
13. Altitude and area of an equilateral triangle (Review Exercise 15 Q2) 30 questions
14. Pythagorean triples (Part 1) 21 questions
15. Worked Examples 1-4 of Unit 15 30 questions
16. Finding an unknown leg (whole-number results) (Part 2) 24 questions
17. Rectangle: diagonal and sides (Part 2) 23 questions
18. Pythagorean triples (Part 2) 20 questions
19. Proof of Pythagoras' theorem: construction and similar triangles 20 questions
20. Rhombus and its diagonals 30 questions
21. Right triangles: area, perimeter and isosceles right triangles 30 questions
22. Finding the hypotenuse (whole-number results) (Part 2) 25 questions
23. Square: diagonal, side and area 30 questions
24. Finding the hypotenuse: surd results 29 questions
25. Rectangle: diagonal and sides (Part 1) 23 questions
26. Quadrilateral with perpendicular diagonals (Review Exercise 15 Q4) 22 questions
27. Exercise 15.1, Review Exercise 15 and unit summary 22 questions
28. Ladders and walls (Exercise 15.1 Q3-Q4) 25 questions

Sample questions: Pythagoras' Theorem

10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.

Q1. The book says the side opposite angle A is denoted

• A. b
• B. h
• C. a(correct answer)
• D. c

Answer: C.We always denote the side opposite angle A as a, opposite B as b and opposite C as c.

Q2. Which side is always the longest in a right-angled triangle?

• A. a leg
• B. the base
• C. the perpendicular
• D. the hypotenuse(correct answer)

Answer: D.Since the hypotenuse squared equals the sum of the other squares, it exceeds each.

Q3. Pythagoras' theorem states that in a right-angled triangle the square of the length of the hypotenuse is equal to

• A. the difference of the squares of the other two sides
• B. the product of the other two sides
• C. the sum of the squares of the lengths of the other two sides(correct answer)
• D. the sum of the lengths of the other two sides

Answer: C.Theorem 15.1. The correct answer is: the sum of the squares of the lengths of the other two sides.

Q4. If (3, 4, 5) is a Pythagorean triple then (6, 8, 10) is also a triple because

• A. multiplying each member by 2 keeps the relation(correct answer)
• B. adding 3 to each member keeps the relation
• C. every set of even numbers is a triple
• D. 6 + 8 > 10

Answer: A.Scaling all sides by the same factor scales the squares by that factor squared.

Q5. A triangle has sides 30 cm, 40 cm and 55 cm. It is

• A. acute-angled
• B. right-angled
• C. obtuse-angled(correct answer)
• D. equilateral

Answer: C.30² + 40² = 2500 and 55² = 3025; since 3025 > 2500 the triangle is obtuse-angled.

Q6. The diagonal of a rectangle measures 6.5 cm and its width is 2.5 cm. The length is

• A. 6 cm(correct answer)
• B. 9 cm
• C. 4 cm
• D. 7 cm

Answer: A.Length² = 6.5² − 2.5² = 42.25 − 6.25 = 36, length = 6 cm (Review Exercise 15 Q1 i).

Q7. The sides of a triangle have lengths x, x + 4 and 20. If the longest side is 20, the value of x that makes it right-angled is

• A. 16
• B. 12(correct answer)
• C. 8
• D. 10

Answer: B.x² + (x + 4)² = 400 gives x² + 4x − 192 = 0, (x + 16)(x − 12) = 0, x = 12 (Review Exercise 15 Q5).

Q8. The sides of a rectangular swimming pool are 50 m and 30 m. The distance between opposite corners is

• A. 40 m
• B. 10√34 m(correct answer)
• C. 80 m
• D. √1600 m

Answer: B.50² + 30² = 3400 = 100 × 34, so the diagonal is 10√34 m ≈ 58.3 m (Exercise 15.1 Q7).

Q9. The summary of Unit 15 states that in a right-angled triangle the square of the hypotenuse equals

From your book: see this page (page 291) Full page Open book

• A. the sum of the other two sides
• B. the product of the other two sides
• C. the difference of the squares
• D. the sum of the squares of the other two sides(correct answer)

Answer: D.Summary bullet. The correct answer is: the sum of the squares of the other two sides.

Q10. Exercise 15.1 Q7 gives the answer 10√34 m for the diagonal of a

• A. rectangular swimming pool 50 m by 30 m(correct answer)
• B. ladder against a wall
• C. square pool of side 30 m
• D. isosceles triangle of base 50 m

Answer: A.50² + 30² = 3400. The correct answer is: rectangular swimming pool 50 m by 30 m.