HiSet: High School Equivalency Test: Math - Prove relationships in geometric figures

$\bigtriangleup ABC \sim \bigtriangleup DEF$ with scale factor 5:4, with $\bigtriangleup ABC$ the larger triangle.

Complete the sentence: the area of $\bigtriangleup ABC$ is _______% greater than that of $\bigtriangleup DEF$ .

(Select the closest whole percent)

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\frac{AB}{DE} = \frac{BC}{EF}$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\frac{AB}{DE} = \frac{BC}{EF}$ and $\angle B \cong \angle E$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\frac{AB}{DE} = \frac{BC}{EF}$ and $\angle C \cong \angle F$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\angle C \cong \angle F$ and $\angle A \cong \angle D$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

A triangle has sides of length 8 and 12; the triangle is scalene and obtuse. Which of the following could be the length of its third side?

$\bigtriangleup ABC \sim \bigtriangleup DEF$ with scale factor 4:5, with $\bigtriangleup ABC$ the smaller triangle.

Complete the sentence: the area of $\bigtriangleup ABC$ is _______% less than that of $\bigtriangleup DEF$ .

(Select the closest whole percent).

$\bigtriangleup ABC \sim \bigtriangleup DEF$ with scale factor 5:4, with $\bigtriangleup ABC$ the larger triangle.

Complete the sentence: the perimeter of $\bigtriangleup ABC$ is _______% greater than that of $\bigtriangleup DEF$ .

(Select the closest whole percent).

$\bigtriangleup ABC \sim \bigtriangleup DEF$ with scale factor 4:5, with $\bigtriangleup ABC$ the smaller triangle.

Complete the sentence: the perimeter of $\bigtriangleup ABC$ is _______% less than that of $\bigtriangleup DEF$ .

(Select the closest whole percent)

Prove relationships in geometric figures