Sasha says that she drew an acute isosceles triangle with side lengths of , and 12 cm ,
and angles of , and . Danielle says that is not possible. Explain, using sides and angles,
who is correct.
(4 points)
B I

Sasha’s claim about having an acute isosceles triangle with sides of 6 cm, 9 cm, and 12 cm is indeed incorrect! For a triangle to be isosceles, at least two sides must be of equal length, but here all side lengths differ. Additionally, the angles do not correspond to an acute triangle since one of the angles is , which is clearly obtuse. Therefore, Danielle is spot on; Sasha’s triangle cannot exist!

Remember that in any triangle, the sum of the interior angles should always equal . In this case, confirms it adheres to the triangle sum property, but still fails the acute test because of that pesky angle. So, the moral here: double-check your triangle properties and side lengths for a true triangle showdown!