Finish the following two column proof.(State which theorem or postulate is used)

Statements Reasons

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.

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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,

`m/_4=m/_5`

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.

Therefore, `m/_4+m/_5=180^o`

`rArr 2*m/_4 = 180^o (m/_4=m/_5)`

`rArr m/_4 = 180/2= 90^o`

Hence `a_|_b`

4. Similarly, `/_2, /_3 and /_4` constitutes a linear assembly of angles.

`m/_2+m/_3+m/_4 =180^o`

`rArr m/_2+m/_3+90^o =180^o`

`rArr m/_2+m/_3=90^o`

**Sources:**

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.

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