Finish the following two column proof.(State which theorem or postulate is used) Statements Reasons 1. <4...
Finish the following two column proof.(State which theorem or postulate is used)
1. <4 `cong` <5 1. Given
2. a`_|_` b 2.________
3. _______ 3.________
4.m<2 +m<3 = 90 degrees 4.________
Thank you for your help.
1. `/_4 cong /_5` 1. Given
2. `a _|_ b` 2. If two lines meet to form congruent adjacent angles then the lines are perpendicular.
3. `/_2 ` is complementary to `/_3` 3. If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary.
4. `m/_2+m/_3=90` 4. Definition of complementary.
Given that `/_4` and `/_ 5` are congruent`
1. To prove that `a_|_b`
According to the congruent angle measure axiom, two congruent angles have the same measure. Thus,
Again linear pair of angles theorem requires that two adjacent angles wil form a linear pair of angles if their nn common arms are two opposite rays.
Here, /_4 and /_5 have a common vertex, a common arm, and their noncommon arms are two opposite rays. hence they are adjacent angles, forming a linear pair.
`rArr 2*m/_4 = 180^o (m/_4=m/_5)`
`rArr m/_4 = 180/2= 90^o`
4. Similarly, `/_2, /_3 and /_4` constitutes a linear assembly of angles.
`rArr m/_2+m/_3+90^o =180^o`