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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 mZ1mZ4 mZEHF 90 mL GHE Given 90 mZEHF mZGHE mZEHF mZ1 m2 mZGHF m2 3 m24 m2 1 m2 2 m3 m24 Substitution class=

Respuesta :

We are given the following information

[tex]\begin{gathered} m\angle1=m\angle4 \\ m\angle EHF=90\degree\: \text{and}\: m\angle GHF=90\degree \end{gathered}[/tex][tex]m\angle EHF=m\angle GHF\qquad \text{reason}=right\text{ angles are equal}[/tex][tex]\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}[/tex]

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

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

Now what is left is

[tex]m\angle2=m\angle3\qquad \text{reason}=angles\text{ are equal}[/tex]

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