Similarity (dilations, AA, proportional segments) Knowledge-Based Download PDF

Questions

1. 1.

   In $\triangle ABC$, segment $AD$ bisects $\angle BAC$ with point $D$ lying on side $BC$. If $AB = 12$, $AC = 18$, and $BC = 15$, what is the length of segment $BD$?

   • A) 5
   • B) 6
   • C) 9
   • D) 10
2. 2.

   In trapezoid $ABCD$ with bases $AB$ and $CD$ parallel to each other, 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) 8
   • B) 10
   • C) 12
   • D) 14
3. 3.

   In $\triangle ABC$, point $D$ lies on segment $AC$ such that $\angle ABD \cong \angle ACB$. If $AD = 4$ and $DC = 5$, what is the length of segment $AB$?

   • A) 6
   • B) $2\sqrt{5}$
   • C) 7.2
   • D) 4.5
4. 4.

   A dilation centered at the origin maps the point $A(6, -9)$ to $A'(10, -15)$. What is the length of segment $B'C'$ if the pre-image segment $BC$ has a length of 18 under the same dilation?

   • A) 22
   • B) 24
   • C) 27
   • D) 30
5. 5.

   In $\triangle ABC$, point $D$ lies on side $AB$ and point $E$ lies on side $AC$ such that segment $DE$ is parallel to side $BC$. If $AD = 6$, $DB = 9$, and $AE = 8$, what is the length of segment $EC$?

   • A) 4
   • B) 10
   • C) 12
   • D) 20