Question:
Andrea is given AABC 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 Andred should
do in order to prove that AABC is a right triangle?
1) Show that a² + b2 = c2, so ZA ZR. This means AABC = ARTS, and so ZC is a right angle
and so AABC is a right triangle.
2) Show that c = 2, so AABC = ARTS and so ZC = ZS. This means ZC is a right angle, and so
AABC is a right triangle.
3) Show that c = x, so AABC = ARTS and so ZCZ ZS. This means ZC is a right angle, and so
ABC is a right triangle.
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4) Show that c = r, so AABC ~ ARTS and so ZC ~ ZS. This means ZC is a right angle, and so
AABC is a right triangle.
Answer:
The correct option is;
2) 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
Explanation:
Here, we have that the given sides of the triangle are a, b and c and therefore, whereby Andrea is able to draw the two sides of the right triangle with sides = a and b and the third, hypotenuse, side as equal to 2, we know that 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.