5-9: Overlapping Triangles and Double Proofs Proof Geometry

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.

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

Your Turn: Given: Prove:

Homework pg. 164 - 166: #1-7odd, 8, 12, 18, 19