Sasha says that she drew an acute isosceles triangle with side lengths of $$ 6 \mathrm{~cm}, 9 \mathrm{~cm} $$, and 12 cm , and angles of $$ 30^{\circ}, 50^{\circ} $$, and $$ 100^{\circ} $$. Danielle says that is not possible. Explain, using sides and angles, who is correct. (4 points) B I $$ \quad \underline{ ext { B }}: \equiv \mathrm{I} $$

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Sasha says that she drew an acute isosceles triangle with side lengths of $$ 6 \mathrm{~cm}, 9 \mathrm{~cm} $$, and 12 cm , and angles of $$ 30^{\circ}, 50^{\circ} $$, and $$ 100^{\circ} $$. Danielle says that is not possible. Explain, using sides and angles, who is correct. (4 points) B I $$ \quad \underline{	ext { B }}: \equiv \mathrm{I} $$

UpStudy AI · Accepted Answer

Danielle is correct. Here's why:

1. **Isosceles Triangle Check**:
   - An isosceles triangle must have at least two equal sides.
   - Sasha's triangle has sides of 6 cm, 9 cm, and 12 cm, all of which are different. Therefore, it is **not** isosceles.

2. **Acute Triangle Check**:
   - An acute triangle requires all angles to be less than $$90^{\circ}$$.
   - Sasha lists the angles as $$30^{\circ}$$, $$50^{\circ}$$, and $$100^{\circ}$$. The $$100^{\circ}$$ angle is **obtuse**, not acute.

Because the triangle is neither isosceles nor acute as Sasha described, Danielle is correct in stating that Sasha's triangle is not possible.

**Conclusion**: Danielle is correct because the given sides do not form an isosceles triangle and the angles include an obtuse angle.
Danielle is correct because Sasha's triangle has all sides of different lengths and includes an obtuse angle of $$100^{\circ}$$, which means it is neither isosceles nor acute.

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