Unit 8 test: Similarity

$\triangle ABC \sim \triangle DEF$ with $AB = 10$, $BC = 15$ and $DE = 4$. Find $EF$.

Which pair of figures is always similar?

Two pentagons are similar with scale factor $\dfrac54$ from the smaller to the larger. The smaller pentagon has perimeter $28$. What is the perimeter of the larger pentagon?

In $\triangle ABC$, $m\angle A = 45^\circ$ and $m\angle B = 65^\circ$. In $\triangle PQR$, $m\angle P = 65^\circ$ and $m\angle R = 70^\circ$. Which statement is correct?

A pole $2$ m tall casts a shadow $5$ m long. At the same time, a building casts a shadow $40$ m long. How tall is the building, in meters?

$\overline{AB} \parallel \overline{DE}$, and segments $\overline{AE}$ and $\overline{BD}$ cross at $C$. If $AC = 4$, $CE = 10$ and $DE = 15$, find $AB$.

A triangle has sides $6$, $9$ and $12$. Another triangle has sides $8$, $12$ and $16$. Which is true?

In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$, $AB = 5$, $AC = 8$ and $DE = 7.5$. What must $DF$ be for $\triangle ABC \sim \triangle DEF$ by SAS?

Which set of facts does not prove $\triangle JKL \sim \triangle MNP$?

In $\triangle ABC$, $\overline{DE} \parallel \overline{BC}$ with $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$. If $AD = 6$, $DB = 4$ and $AE = 9$, find $EC$.

In $\triangle ABC$, $\overline{DE} \parallel \overline{BC}$ with $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$. If $AD = 5$, $DB = 10$ and $BC = 18$, find $DE$.

In $\triangle ABC$, $D$ is on $\overline{AB}$ and $E$ is on $\overline{AC}$. For which lengths is $\overline{DE} \parallel \overline{BC}$?

In $\triangle ABC$, $AB = 12$, $AC = 18$ and $BC = 25$. The bisector of $\angle A$ meets $\overline{BC}$ at $D$. Find $BD$.

In right triangle $ABC$ with right angle at $C$, altitude $\overline{CD}$ meets hypotenuse $\overline{AB}$ at $D$. If $AD = 4$ and $DB = 16$, find $CD$.

In right triangle $ABC$ with right angle at $C$, altitude $\overline{CD}$ meets hypotenuse $\overline{AB}$ at $D$. If $AD = 5$ and $DB = 15$, find $AC$.