5.6 Warm up Find the value of x. 1. 2. 55 0 40 0 x + 83 3. QRS LMN. Name all pairs of congruent corresponding parts. Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, give the triangle congruence statement and state the congruence theorem you would use.
Geometry 5.6 Proving Triangle Congruence by S and S
Essential Question What can you conclude about two triangles when you know certain parts are congruent? 5.6 Proving Triangles Congruent: S, S
Goals Use S and S postulates to prove two triangles are congruent. Solve problems using congruence postulates. 5.6 Proving Triangles Congruent: S, S
Included Sides C C is included between and C. B B is included between and B. CB is included between C and B. 5.6 Proving Triangles Congruent: S, S
Included ngles Y is included between XY and ZY. Z is included between ZX and ZY. X is included between XY and ZX. 5.6 Proving Triangles Congruent: S, S
Theorem 5.10: ngle-side-ngle If two angles and the included side of one triangle are congruent to corresponding parts of another triangle, then the triangles are congruent. (S) C Z B X BC XYZ 5.6 Proving Triangles Congruent: S, S Y
Example 1 Prove DB CBD D C S Statements 1. DB CBD 2. DB DB 3. BD CDB 4. DB CBD Reasons 1. Given 2. Reflexive 3. Given 4. S B 5.6 Proving Triangles Congruent: S, S
Theorem 5.11: ngle-ngle-side If two angles and a non-included side of one triangle are congruent to corresponding parts of another triangle, then the triangles are congruent. B E C F D BC DEF 5.6 Proving Triangles Congruent: S, S
Example 2 re the triangles congruent? If yes, write the triangle congruence statement and give the reason. S B D Yes, BC DC C by S 5.6 Proving Triangles Congruent: S, S
re these triangles congruent? Yes. Reason: S OR S. 5.6 Proving Triangles Congruent: S, S
re these triangles congruent? You could even use S. 5.6 Proving Triangles Congruent: S, S
Overlapping Triangles B C D 5.6 Proving Triangles Congruent: S, S
Example 3 Is BD DC? YES by S B C 85 85 15 15 D 5.6 Proving Triangles Congruent: S, S
Example 3 Is BD DC? YES by S B C 85 85 B 85 C 85 15 15 D 15 15 D 5.6 Proving Triangles Congruent: S, S
Methods to show triangles congruent: SSS SS S S When trying to determine if triangles are congruent, carefully study the given information, mark the triangles if necessary, then determine what pattern you have. 5.6 Proving Triangles Congruent: S, S
Example 4 What other congruence must be given to show that BC RST using the S postulate? B S S T BC ST S C R 5.6 Proving Triangles Congruent: S, S
Example 4 lternate Solution What other congruence must be given to show that BC RST using the S postulate? T B SR S B S C R S 5.6 Proving Triangles Congruent: S, S
Example 5 What other congruence must be given to show that BC RST using the S postulate? B T C RT S S C S R 5.6 Proving Triangles Congruent: S, S
Your Turn For each of the next 4 problems, state the third congruence that must be given to prove BC DEF using the given theorem. 4 Minutes 5.6 Proving Triangles Congruent: S, S
Your Turn 1. S B F D C C F E 5.6 Proving Triangles Congruent: S, S
Your Turn 2. S B E D C C F F 5.6 Proving Triangles Congruent: S, S
Your Turn 3. SSS C B D E F CB FE 5.6 Proving Triangles Congruent: S, S
Your Turn 4. SS F E B C D D 5.6 Proving Triangles Congruent: S, S
Your Turn For each of the next 3 problems, Determine if it is possible to prove the two triangles congruent. If so, write the triangle congruence statement and give the reason. 4 Minutes 5.6 Proving Triangles Congruent: S, S
Your Turn 5 W Yes, WXY WZY by S X Y Z 5.6 Proving Triangles Congruent: S, S
Your Turn 6. C Yes WXY WZY SS D R 5.6 Proving Triangles Congruent: S, S
Your Turn 7. S F T O L The only other thing we know for sure: SOT LOF (Vertical ngles) But this spells SS NOT CONGRUENT 5.6 Proving Triangles Congruent: S, S
Your Turn 8. Fill in the reasons. L R S Given: L SN, LR NR Statements N Prove: LR NSR Reasons 1. L SN 1. Given 2. L N 2. lt. int s 3. LR NR 3. Given 4. LR NRS 4. Vert s 5. LR NSR 5. S 5.6 Proving Triangles Congruent: S, S
List four ways to show triangles are congruent. SSS S SS S List one way that won t work. SS 5.6 Proving Triangles Congruent: S, S
Important! To show two triangles congruent, at least one side must be known. Three angles () does not show congruence (but it is still useful). 5.6 Proving Triangles Congruent: S, S
ssignment 5.6 Proving Triangles Congruent: S, S