Similarity (dilations, AA, proportional segments) Knowledge-Based Practice

Questions

1. 1.

   A dilation with scale factor $k = \frac{5}{2}$ maps $\triangle ABC$ to $\triangle DEF$. If the perimeter of $\triangle DEF$ is 45 and two sides of $\triangle ABC$ have lengths 6 and 7, what is the length of the third side of $\triangle ABC$?

   • A) 4
   • B) 5
   • C) 7.5
   • D) 10
2. 2.

   In right triangle $ABC$ with right angle at vertex $C$, altitude $CD$ is drawn to hypotenuse $AB$. If $AD = 4$ and $DB = 5$, what is the length of segment $AC$?

   • A) 6
   • B) $2\sqrt{5}$
   • C) $3\sqrt{5}$
   • D) 4.5
3. 3.

   In trapezoid $ABCD$ with bases $AB \parallel CD$, the diagonals $AC$ and $BD$ intersect at point $E$. If $AB = 6$, $CD = 15$, and $AE = 4$, what is the length of segment $EC$?

   • A) 6
   • B) 10
   • C) 12
   • D) 14
4. 4.

   In $\triangle PQR$, point $S$ lies on side $PQ$ and point $T$ lies on side $PR$ such that $\angle PST = \angle PRQ$. If $PS = 3$, $SQ = 5$, and $PT = 4$, what is the length of segment $TR$?

   • A) $\frac{8}{3}$
   • B) 2
   • C) $\frac{20}{3}$
   • D) 6
5. 5.

   In $\triangle ABC$, point $D$ lies on side $AB$ and point $E$ lies on side $AC$ such that $DE \parallel BC$. If $AD = 4$, $DB = 6$, and $BC = 15$, what is the length of segment $DE$?

   • A) 10
   • B) 9
   • C) 6
   • D) 5

Answers and step-by-step solutions appear after you finish the test.