Answer:
2. Definition of supplementary angles
3. [tex]\angle 1 + \angle 2 = \angle 1 + \angle 3[/tex]
4. [tex]\angle 2 = \angle 3[/tex]
5. Definition of congruent angles
Step-by-step explanation:
Required
Fill in the gaps
1. Given
Supplementary angles: [tex]\angle 1[/tex] and [tex]\angle 2[/tex]
Supplementary angles: [tex]\angle 1[/tex] and [tex]\angle 3[/tex]
2. Supplementary angles add up to 180.
So:
[tex]\angle 1 + \angle 2 = 180[/tex]
[tex]\angle 1 + \angle 3 = 180[/tex]
3. Apply transitive property on (2)
[tex]\angle 1 + \angle 2 = 180[/tex] and [tex]\angle 1 + \angle 3 = 180[/tex], then
[tex]\angle 1 + \angle 2 = \angle 1 + \angle 3[/tex]
4. Subtract [tex]\angle 1[/tex] from both sides
[tex]\angle 1 - \angle 1 + \angle 2 = \angle 1 + \angle 3 - \angle 1[/tex]
[tex]\angle 1 - \angle 1 + \angle 2 = \angle 1 - \angle 1+ \angle 3[/tex]
[tex]\angle 2 = \angle 3[/tex]
This property is called the subtraction property
5. If [tex]\angle 2 = \angle 3[/tex],
Then [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are congruent
