Geometry Proofs Help - Get Ready For Monday Exam!

In summary, Geometry Proofs can be a difficult subject to understand and to do. If you have any questions, feel free to post them and I will try to help you as best as I can.
  • #1
ccseagle
24
0
Geometry Proofs.. Help!

Please please someone help me! :eek: I have a Geometry Exam on Monday and I don't understand proofs one bit :cry: ! If someone could help me with a few proofs that would be so awesome!
 
Physics news on Phys.org
  • #2
ccseagle said:
Please please someone help me! :eek: I have a Geometry Exam on Monday and I don't understand proofs one bit :cry: ! If someone could help me with a few proofs that would be so awesome!

Have you got any specific questions?
 
  • #3
yeah, could you help me with this proof..

Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

Prove: line AB is congruent to line DE

Picture:

<--A---B---C---D---E-->
 
  • #4
yeah, could you help me with this proof..

Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

Prove: line AB is congruent to line DE

Picture:

<--A---B---C---D---E-->
 
  • #5
Ok, I'll give a hint. You know that [tex]|\vec{AC}|=|\vec{CE}|[/tex] so start with this, then express both sides of the equation in terms of two new lengths. Have a go, and post your thoughts.
 
  • #6
AB+BC= line AC

and

CD+CE = line CE

I don't know, am I even on the right track??
 
  • #7
Yes, so now the equation becomes:[tex]|\vec{AC}|=|\vec{CE}| \Rightarrow
|\vec{AB}|+|\vec{BC}|=|\vec{CD}|+|\vec{DE}|
[/tex] Carry on with this.
 
  • #8
umm.. would the reason be substitution??
 
  • #9
Line AC is congruent to line CE??
 
  • #10
Ok, my notation
[tex]|\vec{AC}|=|\vec{CE}| [/tex]
means that the length of the line AC is equal to the length of the line CE (this is equivalent to the two lines being congruent).

We know that AC is congruent to CE, since C is the midpoint of AE. CAn you say anything similar regarding the lines BC and CD
 
  • #11
C is the midpoint of lines BC and CD?
 
  • #12
WEll, C is the midpoint of BD, therefore BC and CD are congruent. Now look at the equation given in post #7. What does this tell you?
 
  • #13
I don't think I understand.. Can you give me a hint??
 
  • #14
ccseagle said:
I don't think I understand.. Can you give me a hint??

Not without giving you the answer! Ok, here goes: The equation can be rearranged to give

[tex]|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|[/tex]
Now, since the BC and CD are congruent, what can say about the RHS of the equation? What does this then imply?
 
  • #15
I don't know.. Umm what's a RHS??
 
  • #16
Right hand side. Ok, if two lines are congruent, then it means they have the same length. Let's call this length x. Then the RHS is x-x=...?
 
  • #17
the lengths are congruent?
 
  • #18
Well, [tex]|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|=0 \Rightarrow |\vec{AB}|=|\vec{DE}|[/tex]

And so, the lines AB and DE are congruent.
 
  • #19
Ok, i think i get it.. Thanks.. Do you think you could help me with a couple more??
 
  • #20
Maybe one, it's getting quite late. Post your attempt at a proof to the problem you post first though.
 
  • #21
ok, thanks..

Given: angle 8 and angle 1 are supplementary

Prove: angle 4 is congruent to angle 6

Picture:


___________________________________________

-angle 1 is congruent to angle 3 because they are vertical angles
-angle 8 is congruent to angle 6 because they are vertical angles
 

Attachments

  • IMG_0599.jpg
    IMG_0599.jpg
    15 KB · Views: 475
  • #22
-supplementary means that the sum of two angles equals 180 degrees
-angle 8 and angle 1 are congruent because of corresponding angles
 
  • #23
But now is where I get stuck
 
  • #24
Umm, can you give me a hint please??
 
  • #25
ccseagle said:
-supplementary means that the sum of two angles equals 180 degrees
-angle 8 and angle 1 are congruent because of corresponding angles

Careful.. You said 8 and 1 were supplementary!

From what we are given, and your points in your previous post,

6=8=180-1

Now, since 1 and 2 are angles on a line, what can you say about 2 in terms of 1? how is 2 related to 4?
 
  • #26
-angle 2 and angle 4 are vertical angles
-angle 2 and angle 1 is a linear pair
 
  • #27
but also in my given it says that angle 1 and angle 8 are supplementary...
 
  • #28
Yes, so 2=180-1 and 2=4. Put these into the eqn above
 
  • #29
the equation in post #25??

and i don't understand wut u mean.. how do i put into the equation above??
 
Last edited:
  • #30
yes 6=8=180-1
 
  • #31
is this right?

6=8=179??
 
  • #32
No sorry, 1 was the angle: 6=8=180-1=2=4. Hence 6 is congruent to 4.
 
  • #33
ooohh.. so we solved it??
 
  • #34
yup we sure did
 
  • #35
wow! well thanks, you helped alot.. well, i guess i'll let you go now.. Thank you SO MUCH! :):):):):)
 
<h2>1. What are geometry proofs?</h2><p>Geometry proofs are a logical argument that uses a series of statements and previously proven theorems to arrive at a conclusion. They are used to prove the validity of geometric concepts and relationships.</p><h2>2. How do you write a geometry proof?</h2><p>To write a geometry proof, you must start with the given information and use theorems, definitions, and postulates to make logical deductions and arrive at the desired conclusion. It is important to clearly state each step and justify it using the appropriate reasoning.</p><h2>3. What are some common theorems used in geometry proofs?</h2><p>Some common theorems used in geometry proofs include the Pythagorean Theorem, the Angle Bisector Theorem, and the Triangle Sum Theorem. These theorems help to establish relationships between different geometric figures and properties.</p><h2>4. How can I prepare for a geometry proofs exam?</h2><p>To prepare for a geometry proofs exam, it is important to review key concepts and theorems, practice writing proofs, and work through example problems. It can also be helpful to create flashcards or study guides to reinforce important information.</p><h2>5. What are some tips for writing a successful geometry proof?</h2><p>Some tips for writing a successful geometry proof include carefully reading the given information, identifying any theorems or postulates that can be applied, and clearly stating each step and justification. It is also important to double-check your work and make sure your proof is well-organized and easy to follow.</p>

1. What are geometry proofs?

Geometry proofs are a logical argument that uses a series of statements and previously proven theorems to arrive at a conclusion. They are used to prove the validity of geometric concepts and relationships.

2. How do you write a geometry proof?

To write a geometry proof, you must start with the given information and use theorems, definitions, and postulates to make logical deductions and arrive at the desired conclusion. It is important to clearly state each step and justify it using the appropriate reasoning.

3. What are some common theorems used in geometry proofs?

Some common theorems used in geometry proofs include the Pythagorean Theorem, the Angle Bisector Theorem, and the Triangle Sum Theorem. These theorems help to establish relationships between different geometric figures and properties.

4. How can I prepare for a geometry proofs exam?

To prepare for a geometry proofs exam, it is important to review key concepts and theorems, practice writing proofs, and work through example problems. It can also be helpful to create flashcards or study guides to reinforce important information.

5. What are some tips for writing a successful geometry proof?

Some tips for writing a successful geometry proof include carefully reading the given information, identifying any theorems or postulates that can be applied, and clearly stating each step and justification. It is also important to double-check your work and make sure your proof is well-organized and easy to follow.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
16
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
764
  • Introductory Physics Homework Help
Replies
6
Views
760
Replies
1
Views
391
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Differential Geometry
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
13
Views
3K
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
Back
Top