Test Questions: Finding Missing Side Measures Using Similar Triangles

📚 Quick Study Guide

• 📐 Similar Triangles: Triangles are similar if their corresponding angles are congruent and their corresponding sides are in proportion.
• 比例 Corresponding Sides: These are the sides that are in the same relative position in similar triangles.
• ➗ Proportion: A statement that two ratios are equal. For example, if $\triangle ABC \sim \triangle XYZ$, then $\frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX}$.
• 💡 Finding Missing Sides: Set up a proportion using corresponding sides of the similar triangles. Cross-multiply and solve for the unknown side length.
• 📏 Scale Factor: The ratio of the lengths of corresponding sides in similar triangles is called the scale factor.

Practice Quiz

1. If $\triangle ABC \sim \triangle DEF$, $AB = 6$, $BC = 8$, $DE = 9$, what is the length of $EF$?

   1. 10
   2. 12
   3. 11
   4. 13

2. $\triangle PQR$ and $\triangle STU$ are similar. $PQ = 4$, $QR = 6$, $PR = 8$, and $ST = 6$. What is the length of $SU$?

   1. 9
   2. 10
   3. 12
   4. 11

3. Two similar triangles have corresponding sides of lengths 5 and 10. If the perimeter of the smaller triangle is 15, what is the perimeter of the larger triangle?

   1. 45
   2. 30
   3. 25
   4. 20

4. In $\triangle ABC$, $DE \parallel BC$, $AD = 4$, $DB = 6$, and $AE = 5$. Find the length of $EC$.

   1. 7.5
   2. 6.5
   3. 8
   4. 7

5. If $\triangle LMN \sim \triangle XYZ$, $LM = 3$, $MN = 4$, $LN = 5$, and $XY = 6$, what is the length of $YZ$?

   1. 8
   2. 7
   3. 9
   4. 10

6. The sides of a triangle are 3, 5, and 7. In a similar triangle, the shortest side is 9. What is the length of the longest side of the larger triangle?

   1. 21
   2. 15
   3. 20
   4. 25

7. If $\triangle ABC \sim \triangle ADE$, $AD = 2$, $DB = 3$, $AE = 4$, what is the length of $EC$?

   1. 6
   2. 8
   3. 10
   4. 12