Gwendolyn Said:

Does anyone remember the Geometry acronyms for proofs and theorems?

We Answered:

All of the ones you have mentioned seem to be referring to the triangle congruency theorems. Actually, SSA (side-side-angle) is not a theorem for congruency.
Basically, if you know that two triangles have all the parts of the acronym congruent, then the triangles are congruent. For example, for SAS, if we know that two triangles have two congruent sides and the angle inscribed between them is also congruent, then the two triangles are congruent.
By the way, the valid triangle congruency theorems are
SSS, SAS, ASA, and AAS.

Hilda Said:

What are the steps or techniques in proving theorems in geometry?

We Answered:

Draw a picture.

Jon Said:

Could anyone help me prove these geometry theorems?

We Answered:

Hi!

1) Hmm. I do not know any theorem that states that. Maybe you meant Perpendicular lines are adjacent. They cannot be congruent, for a line is extended on both directions. A line consists of infinite points.

2) Theorem 2.56
>>>If two supplementary angle are congruent then, they are right angles

Given: ?1 ? ?2
?1 and ?2 are supplelmentary

Prove: ?1 and ?2 are right angles


Statements: .................................. Reasons
1) ?1 ? ?2 ----------------------------- Given
2) m1 = m2 ----------------------------- Definition of congruent angles
3) ?1 and ?2 are suppl. ?s ------- Given
4) m?1 + m?2 = 180 --------------- Def. of supplementary ?s
5) m?1 + m?1 = 180 --------------- Law of Substitution
6) 2m?1 = 180 ----------------------- Combination of similar terms
7) m?1 = 90 -------------------------- MPE
8) ?1 is a right ? -------------------- Def. of a right ?
9) m?2 = 90 -------------------------- TPE
10) ?2 is a right ? ------------------ Def. of a right ?

3) Given: ?1 and ?2 are congruent ?s
?1 and 2 form a linear pair

Prove: ?1 and ?2 are right angles


Statements ........................................… Reasons
1) ?1 and ?2 are congruent ?s ---------- Given
2) m?1 = m?2 -------------------------------- Def. of congruent ?s
2) ?1 and 2 are form a linear pair ------- Given
3) ?1 and ?2 are supplementary ?s --- The Supplement Postulate
4) m?1 + m?2 = 180 ----------------------- Def. of suppl. ?s
5) m?1 + m?1 = 180 ----------------------- Law of Substitution
6) 2m?1 = 180 ------------------------------- Combination of similar terms
7) m?1 = 90 ---------------------------------- MPE
8) ?1 is a right ? ---------------------------- Def. of a right ?
9) m?2 = 90 ---------------------------------- TPE
10) ?2 is a right ? -------------------------- Def. of a right ?

4) Theorem 2.72
>>> If two parallel line are cut by a transversal line then, each pair of alternate exterior angle is congruent.

Here's the diagram: http://i735.photobucket.com/albums/ww355…

Given: line1 || line2

Prove: ?a ? ?g


Statements ....................................... Reasons
1) line1 || line2 ---------------------------- Given
2) ?a ? ?e -------------------------------- PCAC Postulate
3) ?e ? ?g -------------------------------- Vertical Angle Theorem
4) ?a ? ?g -------------------------------- Transitivity

Whew! That's hard and too long...but my fave part in Geometry. :)
Hope that helps!

Micheal Said:

geometry theorems??

We Answered:

theorem 6.14
Base angles of every isosceles trapezoid are congruent.
theorem 6.15
Base angles are congruent in every isosceles trapezoid.
theorem 6.16
Diagonals are congruent in every isosceles trapezoid.
theorem 6.18
Diagonals are mutually perpendicular in every kite.
theorem 6.19
One pair of opposite angles are congruent in every kite.

Steven Said:

Can anyone tell me geometry theorems?

We Answered:

Here is an easy to understand basic site for you, check out the links on the left side after the page loads.

http://www.teachnet.ie/tbrophy/

Bill Said:

What is the point of long,drawn out geometry postulates and theorems?

We Answered:

there just there for people going to in to more complex geometry so they can refer to something if they forget the rules of geometry.