Question

Andrea is given triangle ABC and told that a ^ 2 + b ^ 2 = c ^ 2 draws right triangle RTS with legs measuring a and b and hypotenuse measuring Which best describes what Andrea should do in order to prove that triangle ABC is a right triangle?

Answer 1

Complete question is;

Andrea is given ABC and told that a² + b² = c². She draws right triangle RTS with legs measuring a and b and hypotenuse measuring 2. Which best describes what Andrea should

do in order to prove that ABC is a right triangle?

Answer:

Andrea should show that c = 2, so: ∡ABC = ∡RTS and ∡C = ∡S. Hence, ∡C is a right angled triangle, hence ΔABC is a right triangle

Step-by-step explanation:

In this question, we are told that the given sides of the triangle are a, b and c. Now, Andrea is able to draw the two sides of the right triangle with sides = a and b and the third, hypotenuse equal to 2. Since the length of the hypotenuse = 2, then we have;

2² = a² + b²

However, we are told that c² = a² + b²

Therefore, c = 2

Hence, Andrea should show that c = 2 so ΔABC = ΔRTS and ∡C = ∡S hence ∡C is a right angled triangle since it is the angle opposite to the hypotenuse c and therefore, ΔABC is a right triangle.