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Two-Column Proofs with Angles
Many relationships involving angles can be proved by applying rules of Algebra,
as well as the definitions and postulates of Geometry
Example 1)
Given: LEDG  LFDH
Prove: mL1  mL3
Statements
1. LEDG  LFDH
Reasons
1.
2. mLEDG mLFDH
2.
3. mLEDG = mL1 + mL2
MLFDH = mL2 + mL3
3.
4. mL1 + mL2 = mL2 + mL3
4.
5. mL1 = mL3
5.
Example 2)
__ __
Given: AB  BC, mL2  mL3
Prove: mL1 + mL3 = 90
Statements
1. AB  BC, mL2  mL3
Reasons
1.
2. LABC is a right angle
2.
3. mLABC = 90
3.
4. mL ABC = mL1 + mL2
4.
5. mL1 = mL2 = 90
5.
6. mL1 = mL3 = 90
6.
Example 3)
Given: L1 and L2 form a linear pair
mL2 + mL3 + mL4 = 180
Prove: mL1 = mL3 = mL4
Statements
1. L1 and L2 form a linear pair
mL2 + mL3 + mL4 = 180
Reasons
1.
2.
2. linear pairs are supplementary
3. mL1 + mL2 = 180
3.
4.
4. substitution property
5. mL1 = mL3 + mL4
5.
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