Question

geometry proofs using definitions and postulates
name:
date:
class:
1 given: m<kol = m<mon
prove: m<kom = m<lon
statement
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justification

Explanation:

Step1: State the given

$m\angle KOL = m\angle MON$ (Given)

Step2: Observe angle - addition

$m\angle KOL=m\angle KOM + m\angle MOL$ and $m\angle MON=m\angle MOL + m\angle LON$ (Angle - addition postulate)

Step3: Substitute angle - sum expressions

$m\angle KOM + m\angle MOL=m\angle MOL + m\angle LON$ (Substitution property of equality)

Step4: Subtract common angle

$m\angle KOM + m\angle MOL−m\angle MOL=m\angle MOL + m\angle LON−m\angle MOL$ (Subtraction property of equality)

Step5: Simplify

$m\angle KOM = m\angle LON$ (Simplification)

Answer:

Statement	Justification
2. $m\angle KOL=m\angle KOM + m\angle MOL$, $m\angle MON=m\angle MOL + m\angle LON$	Angle - addition postulate
3. $m\angle KOM + m\angle MOL=m\angle MOL + m\angle LON$	Substitution property of equality
4. $m\angle KOM + m\angle MOL−m\angle MOL=m\angle MOL + m\angle LON−m\angle MOL$	Subtraction property of equality
5. $m\angle KOM = m\angle LON$	Simplification