Math Help Geometry Proofs
December 11th, 2006
Question: 8th grade Geometry Proofs Help? ?
I’m not so good with 2 column proofs…>.> Thanks for all the help…:)
1. Given=triangle RSU is equilateral. Line RT bisects angle R
Prove= T is the midpoint of line US
2. Give=Square GHJK. Line GJ bisects angle KGH (oh and the intersection of HK and GJ is angle F or something…)
Prove= triangle GKJ is congruent to GHJ
2 column proofs plz…>.< i suck at math...
Answer: Introduction to the Two-Column Proof
http://en.wikibooks.org/wiki/Geometry/Chapter_2
won’t display corectly.
……Starment,,,Reason
1]angle Line RT bisects angle R……given
2]..RSU is equilateral………………….given
……Lines TS=TU………………Lines RS=SU=UR
…………………………………….STAT 1,STAT 2
2]
……Statment,,,Reason
Square GHJK………………………Given
Line GJ bisects angle KGH…..Given
Line GJ is same in triangle GKJ ,GHJ
angle K~=H,Right angle……..Square GHJK
lines GK~=KJ~=HG~=HJ……Square GHJK
triangle GKJ is congruent to GHJ …180-90-45-45=0deg
……………………………….statment1,2,3,4,5
*Note:
*Congruent
Less formally, two figures are congruent if they have the same shape and size, but are in different positions (for instance one may be rotated, flipped, or simply placed somewhere else).
*Note:
*In geometry, an equilateral triangle is a triangle in which all three sides have equal lengths. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also equal to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.
*Note:
*In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are segment bisectors and angle bisectors.
********
Notes****
**Geometric Proofs **
Terms
*Auxiliary Lines – Lines that are created to help prove a statement.
*Contradiction – The situation that occurs when the negation of a true statement is also true. A contradiction signifies that there has been a mistake in reasoning, and can be used in building indirect proofs.
*Direct Proof – A proof in which the conclusion is drawn directly from previous conclusions, starting with the first statement.
*Geometric Proof – A step-by-step explanation that uses definitions, axioms, postulates, and previously proved theorems to draw a conclusion about a geometric statement. There are two major types of proofs: direct proofs and indirect proofs.
*Indirect Proof – A proof in which a statement is shown to be true because the assumption that its negation is true leads to a contradiction.
*Paragraph Proof – A kind of proof in which the steps are written out in complete sentences, in paragraph form. Identical in content, but different in form, from a two-column proof.
*Two-Column Proof – A kind of proof in which the statements (conclusions) are listed in one column, and the reasons for each statement’s truth are listed in another column. Identical in content, but different in form, from a paragraph proof.
Math Lessons : How to Solve Geometry Proofs
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