Question

I am trying to finish this proof: https://plus.google.com/photos/108114996636423986384/albums/5837916191218978961?authkey=CIOEndrOtoDddg My thinking is: 2)Theorem 3.8, 3) I'm not sure on this one ,4)definition of a right angle. I'd appreciate any help.

Answer 1

Theorem 3.8 conveys no information. That is, 3.8 designates that the theorem is the eighth one in chapter 3 of a book. Ergo, I cannot confirm your answer.

For 2) I would answer as follows: If two lines form congruent adjacent angles, then the lines are perpendicular.

The given proof is missing at least three steps. Did it come from a textbook?

Answer 2

Thank you, it helps me to know if I am at least on the right track. It is a homework assignment that has to be written in only 4 steps. I understand the information you wrote. Theorem 3.8 according to the book: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular - if measurement angle one is congruent to measure angle 2, then g is perpendicular to h. My confusion comes from the fact that when I work it out I have more than 4 steps. Thanks again!

Answer 3

@Walart
"if measurement angle one is congruent to measure angle 2, then g is perpendicular to h."

I do not see lines g and h on the diagram. And, angles 1 and 2 as shown on the diagram cannot be congruent.
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I think that the only thing to do is to combine several steps into one to do this proof. I'll try that and you can check the theorems and postulates against the titles of those in your text. Also - to check whatever work I post shortly.

Answer 4

1) as shown

2) according to above cited book: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular (from @Walart above)

3) <2 and <3 are complementary --> 3) If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

4) m<2 + m<3 = 90 -------------> 4) Definition of Complementary Angles


Walart --> Have you studied this theorem: If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Step 3 is "iffy" in that we need to establish that angles 2 and 3 are acute and adjacent. Some might "eyeball" it but that is not proving.

@Walart --> What do you think?

Answer 5

And thank you!

Answer 6

I see my first reply didn't post so I will submit it again. I am sorry for any confusion, I am new to posting for help. The lines g and h, which I know you figured out, were from the theorem I stated (only I am using lines a and b) I have been working this proof and have come up with the same conclusion you have about step 3. I tried several ways to connect <1 and <s 2 and 3. Your suggestion is, I think the best. I also came up with the same for step 4. Thanks for your help, I really appreciate it!

Answer 7

Glad to help. Geometry is fun.