Question 1

GK∥HJ. Complete the proof that m∠IHK=m∠G+m∠K without using the Triangle Angle Sum Theorem.GKHIJ

GK∥HJ. Complete the proof that m∠IHK=m∠G+m∠K without using the Triangle Angle Sum-example-1

GK∥HJ. Complete the proof that m∠IHK=m∠G+m∠K without using the Triangle Angle Sum-example-2

GK∥HJ. Complete the proof that m∠IHK=m∠G+m∠K without using the Triangle Angle Sum-example-3

Question 2

Explanation

We are given the following:

We are required to prove that:

$m\angle IHK=m\angle G+m\angle K$

We already know that:

$\begin{gathered} GK||HJ\text{ \textbraceleft Given\textbraceright} \\ \\ \angle G\cong\angle IHJ\text{ \textbraceleft Corresponding Angles Theorem\textbraceright} \end{gathered}$

Now, we have:

$\angle K\cong\angle JHK\text{ \textbraceleft Alternate Interior Angles Theorem\textbraceright}$

Also, we have:

$m\angle IHK=m\operatorname{\angle}IHJ+m\operatorname{\angle}JHK\text{ \textbraceleft Additive Property of Angle Measure\textbraceright}$

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