Triangle Sum Theorem Proof

In the formal proof of the triangle sum theorem, the triangle is always formed between ________________________.

• perpendicular lines

• parallel lines

• intersecting lines

• a bunch of points

Each of the following relationships or properties is critical to proving the Triangle Sum Theorem EXCEPT _________.

• $\parallel\rightarrow$ alternate interior angles are $\cong$

• Substitution Property

• Angle Addition Postulate

• Linear Pair Property

Fill in statement #2.

• $m\angle6+m\angle2+m\angle3+m\angle5=360$

• $m\angle1+m\angle4=m\angle6$

• $m\angle1+m\angle2+m\angle3=180$

• $m\angle1+m\angle4+m\angle7=180$

Fill in statement #3.

•  $m\angle7=m\angle2$ 

•  $m\angle1=m\angle6$ 

•  $m\angle1=m\angle3$ 

•  $m\angle4=m\angle5$ 

Fill in reason #3.

•  $\parallel\rightarrow$  corresponding angles are  $\cong$  

• Substitution Property

•  $\parallel\rightarrow$  alternate interior angles are  $\cong$  

• Transitive Property

Fill in statement #4.

•  $m\angle7=m\angle4$ 

•  $m\angle1=m\angle6$ 

•  $m\angle1=m\angle3$ 

•  $m\angle4=m\angle3$ 

Fill in reason #4.

•  $\parallel\rightarrow$ alternate interior angles  are  $\cong$  

• Substitution Property 

•  $\parallel\rightarrow$  corresponding angles are  $\cong$  

• Reflexive Property

Fill in reason #5.

• Triangle Sum Theorem

• Substitution Property 

• Prove

• Reflexive Property