Quick Check: SSS Similarity Quizzes for Geometry Students

📚 Quick Study Guide

• 📐 SSS (Side-Side-Side) Similarity Postulate: If the corresponding sides of two triangles are proportional, then the triangles are similar.
• 📏 To prove similarity using SSS, you must show that $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$, where $\triangle ABC$ and $\triangle DEF$ are the two triangles being compared.
• 💡 Remember to check if the ratios are equal *after* setting up the proportions correctly.
• 🤔 If even one ratio is different, the triangles are *not* similar by SSS.
• 📝 SSS Similarity only proves similarity; it doesn't prove congruence.

Practice Quiz

1. Which of the following conditions must be true for $\triangle ABC \sim \triangle DEF$ by SSS Similarity?

   1. A. $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$
   2. B. $\frac{AB}{DE} = \frac{AC}{EF} = \frac{BC}{DF}$
   3. C. $AB = DE, BC = EF, AC = DF$
   4. D. $\angle A = \angle D, \angle B = \angle E, \angle C = \angle F$

2. If $AB = 4$, $BC = 6$, $AC = 8$, $DE = 6$, $EF = 9$, and $DF = 12$, are $\triangle ABC$ and $\triangle DEF$ similar by SSS?

   1. A. Yes
   2. B. No
   3. C. Cannot be determined
   4. D. Only if the angles are also equal

3. Given $\triangle PQR$ with $PQ = 5$, $QR = 7$, $RP = 10$ and $\triangle XYZ$ with $XY = 2.5$, $YZ = 3.5$, $ZX = 5$, are the triangles similar?

   1. A. Yes
   2. B. No
   3. C. Only if the corresponding angles are congruent
   4. D. Only if the triangles are congruent

4. In $\triangle ABC$, $AB = 3$, $BC = 5$, $CA = 7$. In $\triangle LMN$, $LM = 9$, $MN = 15$, $NL = 20$. Are the triangles similar?

   1. A. Yes
   2. B. No
   3. C. Similar, but not by SSS
   4. D. Cannot be determined

5. $\triangle STU$ has sides $ST = 2$, $TU = 3$, $US = 4$. $\triangle VWX$ has sides $VW = 4$, $WX = 6$, $XV = 8$. Are the triangles similar?

   1. A. Yes
   2. B. No
   3. C. The sides are proportional, but the triangles aren't similar
   4. D. Not enough information

6. If the sides of one triangle are 5, 12, and 13, and the sides of another triangle are 10, 24, and 26, are the triangles similar?

   1. A. Yes
   2. B. No
   3. C. Only if they are right triangles
   4. D. Only if the angle between sides 5 and 12 equals the angle between sides 10 and 24

7. $\triangle DOG$ has sides $DO = 6$, $OG = 8$, $GD = 10$. $\triangle CAT$ has sides $CA = 9$, $AT = 12$, and $TC = 14$. Are the triangles similar by SSS?

   1. A. Yes
   2. B. No
   3. C. Only if the angles are equal
   4. D. Only if they are right triangles