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lilporkchop69
10-17-2009, 09:29 PM
So I'm having some trouble figuring this out. I need to make a two-column proof for this problem, so, if you guys would be so kind as through walk me through this one, that would be greatly appreciated. :)

Given: <3 and <4 are right angles; m<1 = m<2
Prove: ΔABC = ΔABD

http://i831.photobucket.com/albums/zz240/lilporkchop69/TriangleProb1.jpg?t=1255836330
Ace2cool
10-17-2009, 09:44 PM
hint.. consider what you need to prove two triangles congruent

SSS
ASA
SAS
Zapurdead
10-18-2009, 09:10 AM
You have more than two pairs of congruent angles.
Karl
10-18-2009, 11:01 AM
If 3=4 and 1=2 then 5=6. Done.

EDIT: Woops, nevermind. I didn't put into account the side lengths.
skilldude
10-18-2009, 11:04 AM
the angle from D to B are the same from A to B. You gotta do some thinkin
lilporkchop69
10-18-2009, 11:55 AM
the angle from D to B are the same from A to B. You gotta do some thinkin
That made no sense, whatsoever. This is a proof, I'm not solving for anything.
If 3=4 and 1=2 then 5=6. Done.

EDIT: Woops, nevermind. I didn't put into account the side lengths.
<3=<4 is not given to me. Also, the sides don't have a given length, and even if they did, it would be of no use to me.
You have more than two pairs of congruent angles.
So, that makes the triangle an Isosceles triangle... so, I'm guessing the outcome of my proof will be ASA...
hint.. consider what you need to prove two triangles congruent

SSS
ASA
SAS
(You're probably the only one here who knows what he's talking about).
Yes, I have taken that into consideration, but I'm completely lost on how to get from my given, to there. The SAS and all should be the last step, as long as I'm not trying to prove anything else.

Just need somebody to help guide me to the right direction. I don't know where to go from my given, but after some help, I should be able to figure the rest out on my own.

Thanks to all who have posted, for helping me out. :)
DarkReality
10-18-2009, 12:59 PM
<3=<4 is not given to me. Also, the sides don't have a given length, and even if they did, it would be of no use to me.

... They're both right angles? As in... 90 degrees? Both of them? You see where this is going?

The sides may not have any given length, but you don't need any. Look reeeeeal closely at the picture.
lilporkchop69
10-18-2009, 01:07 PM
... They're both right angles? As in... 90 degrees? Both of them? You see where this is going?

The sides may not have any given length, but you don't need any. Look reeeeeal closely at the picture.
D: I wasn't thinking when I posted that.
skilldude
10-19-2009, 05:38 AM
and also the angles from D to B are exactly the same, so that is proof, you don't need numbers to solve that
lilporkchop69
10-19-2009, 05:07 PM
and also the angles from D to B are exactly the same, so that is proof, you don't need numbers to solve that
DB is a LINE. If you were referring to angles 4 and 2, they don't equal the letters. 4 is obviously 90 degrees, as this was given. And you're not supposed to use numbers while solving a proof. Have you ever even made a proof before?
Shawnachu
10-21-2009, 08:48 PM
<3 and <4 are congruent since they're both right angles.
<1=<2 by given
<5 and <6 by 3rd angles thrm (2 < pairs are = says 3rd pair is congruent)
AB=AB by reflexive prop.
ABC=ABD by ASA
game-bot
10-22-2009, 03:22 PM
If you need proof (read: lengths), you can't prove that the two triangles are equal. However, with the angles, you can at least say that the two triangles are similar, since they both have the 90 angle, and <1==<2, which means 5 and 6 must be the same aswell (Triangle Angle Sum Theorem).
Liokae
10-22-2009, 03:38 PM
If you need proof (read: lengths), you can't prove that the two triangles are equal. However, with the angles, you can at least say that the two triangles are similar, since they both have the 90 angle, and <1==<2, which means 5 and 6 must be the same aswell (Triangle Angle Sum Theorem).

You know they're similar, and you know that they have a common side. They're equal.
denacioust
10-22-2009, 03:44 PM
<3=<4 and <1=<2, therefore all the angles in the triangle are the same.
As the line down the middle is common they have one length in common too. Also since the line down the middle bisects the angle (both angles are the same) then it bisects the line at the top, therefore the two lengths there are the same.
Therefore you have 2 sides, 3 angles. More than sufficient proof for congruity.
game-bot
10-22-2009, 03:46 PM
You know they're similar, and you know that they have a common side. They're equal.

Hadn't thought of that. Thanks.
Ace2cool
10-23-2009, 10:12 PM
sigh.

1. BA = BA, by the reflexive property of equality.
2. Angle 3 = angle 4, given
3. Angle 1 = angle 2, given
4. 180 - 90 - angle 1 = angle 5.... 180 degrees in a triangle
5. 180 - 90 - angle 2 = angle 6... 180 degrees in a triangle
6. 90 - angle 1 = angle 5
7. 90 - angle 1 = angle 6, because of substitution (angle 1 for angle 2)
8. ASA - angle 5 is congruent to angle 6, BA = BA, and the right angles are congruent.