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# Chapter 6 project

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N. Smith's Geometry chapter 6 project on proofs for Mrs. Bomberger.

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### Chapter 6 project

1. 1. 6.7 PROBLEM 14 PG. 249Given: Angle PMN is congruent to angle ONM; Angle MPN is congruent to angle NOMProve: Triangle LMO is congruent to triangle LNP
2. 2. STEP 1AN G L E PMN I S CON G RUEN T TOAN G L E ON M; AN G L E MPN ISCON G RUEN T TO AN G L E N OM GIVEN
3. 3. STEP 2TRIANGLE LMN IS ANISOSCELES TRIANGLE; DEFINITION OFLINE LN IS CONGRUENT ISOSCELES TRIANGLETO LINE LM
4. 4. STEP 3LINE MN IS CONGRUENT REFLEXIVE PROPERTY OFTO LINE MN CONGRUENT SEGMENTS
5. 5. STEP 4TRIANGLE MPN IS SAA TRIANGLECONGRUENT TO TRIANGLENOM PO ST U LAT E
6. 6. STEP 5LINE PN IS CONGRUENT TO DEFINITION OFLINE OM, ANGLE 2 ISCONGRUENT TO ANGLE 3 CONGRUENT TRIANGLES
7. 7. STEP 6ANGLE 1 IS CONGRUENT ADJACENT ANGLETO ANGLE 4 PORTION THEOREM
8. 8. STEP 7TRIANGLE LMO IS SAS TRIANGLECONGRUENT TO TRIANGLE PO ST U LAT ENOM
9. 9. 6.8 PROBLEM 18 PG. 255Given: Line RS is congruent to line TS; Line RU is congruent to line TUProve: The measure of angle RSU is 90 degrees
10. 10. STEP 1LINE RS IS CONGRUENT TOLINE TS; LINE RU ISCONGRUENT TO LINE TU GIVEN
11. 11. STEP 2LINE US IS CONGRUENT REFLEXIVE PROPERTY OFTO LINE US CONGRUENT SEGMENTS
12. 12. STEP 3TRIANGLE RUS IS SSS TRIANGLECONGRUENT TO TRIANGLETUS PO ST U LAT E
13. 13. STEP 4ANGLE RSU IS CONGRUENT SSS TRIANGLETO ANGLE TSU PO ST U LAT E
14. 14. STEP 5ANGLE RSU AND ANGLE LINEAR PAIRS ARETSU ARE SUPPLEMENTARY SUPPLEMENTARY
15. 15. STEP 6ANGLE RSU AND ANGLE CONGRUENT SUPPLEMENTSTSU ARE RIGHT ANGLES ARE RIGHT ANGLES
16. 16. STEP 7THE MEASURE OF ANGLE DEFINITION OF RIGHTRSU IS 90 DEGREES ANGLE