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Complete the table to show that mZ2 = m23 들 Equation Reason mZ1=mZ4, mZEHF = 90°, mL GHE Given = 90° mZEHF =mZGHE mZEHF = mZ1 + m2 mZGHF = m2 3 + m24 m2 1 + m2 2 = m/3 + m24 Substitution Property of Equality mZ2 = m23

Complete the table to show that mZ2 = m23 들 Equation Reason mZ1=mZ4, mZEHF = 90°, mL-example-1
User Tamiz
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1 Answer

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22 votes

We are given the following information


\begin{gathered} m\angle1=m\angle4 \\ m\angle EHF=90\degree\: \text{and}\: m\angle GHF=90\degree \end{gathered}
m\angle EHF=m\angle GHF\qquad \text{reason}=right\text{ angles are equal}
\begin{gathered} m\angle EHF=m\angle1+m\angle2\qquad \text{reason}=bisector\text{ angles theorem} \\ m\angle GHF=m\angle3+m\angle4\qquad \text{reason}=bisector\text{ angles theorem} \end{gathered}

Please note that a bisector line divides an angle into two equal angles and their sum will be equal to the original angle.


m\angle1+m\angle2=m\angle3+m\angle4\qquad \text{substitution property}
d\text{.}\: m\angle1=m\angle4

Now what is left is


m\angle2=m\angle3\qquad \text{reason}=angles\text{ are equal}

User Pixunil
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