4.6: Use Congruent Triangles

Properties of Congruent Triangles What pairs of angles and sides are congruent? B C

Using CPCTC: Once you know that triangles are congruent, you can make conclusions about corresponding sides and angles because Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Ex.1: Suppose you know that by SAS. Which additional pairs of sides and angles are congruent by CPCTC? A B D C

Example 2: B D A C <ACB <DCB Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? <ACB <DCB B D A C

Example 3: M N P L O <PLM <PNO Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? <PLM <PNO M N P L O

Example 4: Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? MJ ML K J M L

Example 5: Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? ML ON M N L O

Example 6: Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? BC DA B C A D

Example 7 Is enough information given in the figure to show that the given statement is true?  B C A D E B C

Example 8 Is enough information given in the figure to show that the given statement is true?  A C D A E C B

Given: WZ  YZ and X is the midpoint of WY Prove: W  Y Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. W

Given: QR  SR and PR bisects SRQ Prove: PS  PQ Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. S