In the same 4‑piece arrangement, angle labels near the corners show x and 90 − x at adjacent angles around the boundary. What justifies that each corner angle of the new 4‑sided figure is a right angle, so the figure is a square?
  • Each corner combines angles x and 90 − x to total , giving four right angles
  • Each corner is an exterior angle of triangle V, so it must be
  • Opposite sides are parallel, so each interior angle is
  • Congruence of T, U, W, and X forces all interior angles to be equal but not necessarily right angles
For a right‑angled triangle with shorter sides of lengths 5 cm and 12 cm, what is the length of its hypotenuse?
  • 12 cm
  • 13 cm
  • 14 cm
  • 17 cm
For a right‑angled triangle with one short side of length 8 cm and a hypotenuse of length 17 cm, what is the length of the other short side?
  • 9 cm
  • 12 cm
  • 15 cm
  • 16 cm
Using the paper‑piece construction where the square on the hypotenuse has area equal to the sum of the areas on the legs, how would you construct a square whose area is triple the area of a given square of side ? Choose the legs so that the square on the hypotenuse has area .
  • Use legs and
  • Use legs and
  • Use legs and
  • Use legs and
Using the same method, how would you construct a square whose area is five times the area of a given square of side ? Choose the legs so that the square on the hypotenuse has area .
  • Use legs and
  • Use legs and
  • Use legs and
  • Use legs and
Let a, b, and c denote the side lengths of a right triangle, with c the hypotenuse. If and , what is to one decimal place?
  • 7.8
  • 8.4
  • 8.6
  • 9.0
Let a, b, and c denote the side lengths of a right triangle, with c the hypotenuse. If and , what is ?
  • 10
  • 11
  • 12
  • 13
Which list shows all the Baudhāyana triples whose numbers are less than or equal to 20?
  • (3, 4, 5), (6, 8, 10), (9, 12, 15), (12, 16, 20)
  • (3, 4, 6), (6, 8, 10), (9, 12, 15), (15, 20, 25)
  • (2, 3, 4), (4, 6, 8), (6, 9, 12), (8, 12, 16)
  • (5, 12, 13), (8, 15, 17), (7, 24, 25), (15, 36, 39)
Is there an unending sequence of Baudhāyana triples?
  • Yes, there are infinitely many
  • No, there are only finitely many
Is (30, 40, 50) a Baudhāyana triple?
  • Yes
  • No
Is (300, 400, 500) a Baudhāyana triple?
  • Yes
  • No
Among the triples with numbers less than or equal to 20, what pattern do you observe?
  • Each triple is a multiple of (3, 4, 5)
  • The three numbers in each triple form an arithmetic progression
  • All numbers in each triple are odd
  • Each triple has equal numbers
Based on the observed pattern, which conjecture is correct about Baudhāyana triples?
  • For any positive integer k, (3k, 4k, 5k) is a Baudhāyana triple
  • For any integer k, (k, k, k) is a Baudhāyana triple
  • For any positive integer k, (3k, 5k, 7k) is a Baudhāyana triple
  • For any positive integer k, (k, k + 1, k + 2) is a Baudhāyana triple
Is the conjecture that (3k, 4k, 5k) is a Baudhāyana triple for any positive integer k true?
  • Yes
  • No
Which statement further generalises the pattern about Baudhāyana triples?
  • If (a, b, c) is a Baudhāyana triple, then for any positive integer k, (ka, kb, kc) is also a Baudhāyana triple
  • If (a, b, c) is a Baudhāyana triple, then (a + 1, b + 1, c + 1) is also a Baudhāyana triple
  • If (a, b, c) is a Baudhāyana triple, then (a, b, c + 1) is also a Baudhāyana triple
  • If (a, b, c) is a Baudhāyana triple, then (ka, kb, c) is also a Baudhāyana triple
If (a, b, c) is a Baudhāyana triple, then (ka, kb, kc) is also a Baudhāyana triple for any positive integer k. Is this statement true?
  • True
  • False
Is (5, 12, 13) a primitive Baudhāyana triple?
  • Yes
  • No
Are the scaled versions of primitive Baudhāyana triples themselves primitive?
  • No, scaled versions are non-primitive because they have a common factor greater than 1
  • Yes, scaled versions are always primitive
  • Only if the scale factor is 1
  • Only if the scale factor is a prime number
Which relationship is used to generate more primitive Baudhāyana triples?
  • The sum of consecutive odd numbers equals square numbers
  • The sum of even numbers equals cube numbers
  • The product of two consecutive integers equals a square
  • The difference of consecutive squares equals even numbers only
In the method based on odd numbers, if the nth odd number equals a square , which triple is formed?
  • (n − 1, t, n)
  • (t − 1, n, t)
  • (n, t, n + 1)
  • (t, n − 1, t + 1)
0 h : 0 m : 1 s

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