Question

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

Answer 1

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}`