Examples of congruent triangles SSS

📚 Quick Study Guide

• 📐 SSS (Side-Side-Side) Postulate: If all three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.
• 📏 Congruent Sides: Congruent sides are sides that have the same length. We mark them with tick marks (e.g., one tick mark on each of two sides means they are congruent).
• 📝 Symbol for Congruence: The symbol $\cong$ means 'is congruent to'. So, if $AB \cong DE$, it means side AB is congruent to side DE.
• 💡 Applying SSS: To prove triangles are congruent using SSS, you must show that all three pairs of corresponding sides are congruent.
• 🔍 Example: If triangle ABC has sides AB = 3, BC = 4, CA = 5, and triangle DEF has sides DE = 3, EF = 4, FD = 5, then $\triangle ABC \cong \triangle DEF$ by SSS.

Practice Quiz

1. What does the SSS postulate state about congruent triangles?
   1. A) If two sides and an included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
   2. B) If all three angles of one triangle are congruent to the corresponding angles of another triangle, the triangles are congruent.
   3. C) If all three sides of one triangle are congruent to the corresponding sides of another triangle, the triangles are congruent.
   4. D) If two angles and an included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
2. If $\triangle PQR$ has sides $PQ = 5$, $QR = 7$, $RP = 9$, and $\triangle XYZ$ has sides $XY = 5$, $YZ = 7$, $ZX = 9$, which statement is true based on SSS?
   1. A) $\triangle PQR \cong \triangle ZXY$
   2. B) $\triangle PQR \cong \triangle XZY$
   3. C) $\triangle PQR \cong \triangle YZX$
   4. D) $\triangle PQR \cong \triangle XYZ$
3. In triangles ABC and DEF, $AB \cong DE$, $BC \cong EF$, and $CA \cong FD$. Which postulate proves that $\triangle ABC \cong \triangle DEF$?
   1. A) ASA
   2. B) SAS
   3. C) SSS
   4. D) AAS
4. Which of the following is NOT a condition required to prove triangle congruence using SSS?
   1. A) All three sides of one triangle must be congruent to the corresponding sides of the other triangle.
   2. B) Corresponding angles must be congruent.
   3. C) The sides must be in corresponding order.
   4. D) The triangles must exist in the same plane.
5. If $AB = 6$, $BC = 8$, $CA = 10$ in $\triangle ABC$, and $DE = 6$, $EF = 8$, $FD = 10$ in $\triangle DEF$, what can be concluded?
   1. A) $\triangle ABC$ and $\triangle DEF$ are similar but not congruent.
   2. B) $\triangle ABC \cong \triangle DEF$ by SSS.
   3. C) $\triangle ABC \cong \triangle DEF$ by SAS.
   4. D) $\triangle ABC$ and $\triangle DEF$ are not related.
6. Suppose $\triangle LMN$ and $\triangle OPQ$ have sides $LM = 4$, $MN = 5$, $NL = 6$ and $OP = 4$, $PQ = 5$, $QO = 6$. Which congruence statement is correct?
   1. A) $\triangle LMN \cong \triangle OQP$
   2. B) $\triangle LMN \cong \triangle POQ$
   3. C) $\triangle LMN \cong \triangle QOP$
   4. D) $\triangle LMN \cong \triangle OPQ$
7. Given $\triangle RST$ where $RS = 12$, $ST = 15$, and $TR = 18$, and $\triangle UVW$ where $UV = 12$, $VW = 15$, and $WU = 18$, which statement accurately describes the relationship between the triangles?
   1. A) The triangles are congruent by SAS.
   2. B) The triangles are congruent by SSS.
   3. C) The triangles are similar but not congruent.
   4. D) The triangles cannot be compared.