Question 4 (1 point) (04.01 MC) $$ riangle A B C $$ is located at $$ A(3,1), B(4,4) $$, and $$ C(5,1) $$. Zackery says that $$ riangle A B C $$ is an equilateral triangle, while Verna says that it is an isosceles triangle. Who is correct? a Zackery, because all of the sides are congruent b Zackery, Decause there are no congruent sides c Verna, because $$ \overline{\mathrm{BC}} \cong \overline{\mathrm{AC}} $$ d Verna, because $$ \overline{A B} \cong \overline{\mathrm{BC}} $$

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Question 4 (1 point) (04.01 MC) $$ 	riangle A B C $$ is located at $$ A(3,1), B(4,4) $$, and $$ C(5,1) $$. Zackery says that $$ 	riangle A B C $$ is an equilateral triangle, while Verna says that it is an isosceles triangle. Who is correct? a Zackery, because all of the sides are congruent b Zackery, Decause there are no congruent sides c Verna, because $$ \overline{\mathrm{BC}} \cong \overline{\mathrm{AC}} $$ d Verna, because $$ \overline{A B} \cong \overline{\mathrm{BC}} $$

UpStudy AI · Accepted Answer

To determine whether $$ \triangle ABC $$ is equilateral or isosceles, let's calculate the lengths of its sides using the distance formula:

1. **Side $$ AB $$** between points $$ A(3,1) $$ and $$ B(4,4) $$:
   $$
   AB = \sqrt{(4-3)^2 + (4-1)^2} = \sqrt{1 + 9} = \sqrt{10}
   $$

2. **Side $$ BC $$** between points $$ B(4,4) $$ and $$ C(5,1) $$:
   $$
   BC = \sqrt{(5-4)^2 + (1-4)^2} = \sqrt{1 + 9} = \sqrt{10}
   $$

3. **Side $$ AC $$** between points $$ A(3,1) $$ and $$ C(5,1) $$:
   $$
   AC = \sqrt{(5-3)^2 + (1-1)^2} = \sqrt{4 + 0} = 2
   $$

Since $$ AB = BC = \sqrt{10} $$ and $$ AC = 2 $$, two sides are congruent, which makes $$ \triangle ABC $$ an **isosceles** triangle. Zackery is incorrect because not all sides are congruent, so the correct statement is:

**Answer:**  
**d Verna, because $$ \overline{A B} \cong \overline{\mathrm{BC}} $$**
Verna is correct because sides $$ AB $$ and $$ BC $$ are congruent.

Question 4 (1 point)
(04.01 MC)
is located at , and . Zackery says that is an equilateral triangle, while Verna says that it is an isosceles triangle. Who is correct?
a Zackery, because all of the sides are congruent
b Zackery, Decause there are no congruent sides
c Verna, because
d Verna, because

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Question 4 (1 point) (04.01 MC) is located at , and . Zackery says that is an equilateral triangle, while Verna says that it is an isosceles triangle. Who is correct? a Zackery, because all of the sides are congruent b Zackery, Decause there are no congruent sides c Verna, because d Verna, because