1. 5-9: Overlapping Triangles and Double Proofs
Proof Geometry

2. Example 1
Given: DC=BC, DK=BK Prove: AD=AB Plan for proof. USE COLOR. Step 1:Look for triangles that we know at least 2 or perhaps even 3 things about. In this example CDK and CBK Step 2: Prove them congruent SSS Step 3: Look for triangles that contain the segments or angles we want to prove congruent and that overlap with the triangles in Step 1 – the bigger the overlap the better In this example ADC and ABC Step 4: Use CPCTC to move from the triangles in step 1 to the triangles in Step 3 using the overlap In this example DCA  BCA Step 5: Prove the triangles in Step 3 congruent SAS Step 6: Use CPCTC to prove what we were asked.

3. Now turn your plan into a proof
Statements
Reasons
In CDK and CBK
DC=BC, DK=BK
Given
CK=CK
Reflexive prop. of eq.
CDK  CBK
SSS
In ADC and ABC
DCA  BCA
CPCTC
DC=BC
AC=AC
Reflexive
ADC  ABC
SAS
AD=AB
Given: DC=BC, DK=BK
Prove: AD=AB

4. Your Turn:
Given: Prove:

7. Homework
pg : #1-7odd, 8, 12, 18, 19