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Geometry proof help (perpendicular lines/supplements)?

Hello. Going over a study guide for my geometry test. Came across a few issues. My book isn't much help. Mind explaining it in laymen terms/proofs? 10th grade geometry student.

Here is the first one (the one giving me the most trouble).

Attachment 29258

Here's the second one, I feel like I haven't been given enough information.

Attachment 29259

Thanks a bunch!

Re: Geometry proof help (perpendicular lines/supplements)?

Quote:

Originally Posted by

**Connorzman** Here is the first one (the one giving me the most trouble).

Attachment 29258
Here's the second one, I feel like I haven't been given enough information.

Attachment 29259

The first one depends upon the facts:

Perpendicular lines intersect at **right angles**.

All right angles are congruent.

Congruence is a transitive relation.

The second one depends upon knowing that vertical angles are congruent.

Re: Geometry proof help (perpendicular lines/supplements)?

I understand what you're saying in the first one. But how would I write it in a *two column proof*?

Re: Geometry proof help (perpendicular lines/supplements)?

Quote:

Originally Posted by

**Connorzman** I understand what you're saying in the first one. But how would I write it in a *two column proof*?

I have absolutely no idea.

*Two column proofs* in geometry are for people who don't understand proof.

Re: Geometry proof help (perpendicular lines/supplements)?

1. l perpendicular to n Reason: given

2. angle ABJ is a right angle Reason: definition of "perpendicular"

3. m perpendicular to n Reason: given

4. Angle DCH is a right angle Reason: definition of "perpendicular".

5. Angle ABJ is congruent to angle DCH Reason: all right angles are congruent

6. Angle ABJ is congruent to angle KHL Reason: given

7. Angle KHL is congruent to angle DCH Reason: things congruent to the same thing are congruent to each other.

That is how I would do it. Of course, I do not know exactly what "postulates" and "theorems" you have available to use. For example, it might be that you do NOT (yet) have "all right angles are congruent" but rather that "all right angles have a measure of 90 degrees" and "if two angles have the same measure they are congruent". Of you might not have "two lines are perpendicular if and only if they form right angles" but "if two lines are perpendicular, then they form four angles with measure 90 degrees".

Re: Geometry proof help (perpendicular lines/supplements)?

Re: Geometry proof help (perpendicular lines/supplements)?

Theorem 1 vertical angles are congruent

Practical proof. Draw intersecting lines.Cut out the angles and note they have equal measures

Line proof .Label the opposite angles of intersecting lines 1and 2 and 3 and 4 their supplements.1 and 2 are vertical

m1 +m3 = 180 additive property postulate

m2+m3 = 180 same

m1+m3 =m2+m3 equals to equals are equal to each other

m1=m2 subtract m3 from each side

Re: Geometry proof help (perpendicular lines/supplements)?

Quote:

Originally Posted by

**Plato** I have absolutely no idea.

*Two column proofs* in geometry are for people who don't understand proof.

I second you