Can you please help me with some definitions from Geometry?! It's proving statements in Geometry For each word or expression in Column 1 indicate the letter of the matching definition or...

Can you please help me with some definitions from Geometry?!

It's proving statements in Geometry

For each word or expression in Column 1 indicate the letter of the matching definition or explanation in column 2:

I really hope you understand the way i wrote them out, i couldn't find the symbols so i wrote them out in parenthesis. I also did some of them, I wrote the letters next to them, PLEASE help me with the rest!!

 

COLUMN 1

1.)a=a F

2.)R,ST are collinear points such that RS=ST

(with a line above RS and ST)

3.)AB + BC =AC(with a line above AB, BC, and AC)

4.)a=b : b=a A

5.)A =b , b=c, then a=c C

6.)m<1 = m<2 : then <1 is congruent to <2

7.)M<1 + m<2 ; then 2m<1 = m<1 +m2

8.)ACB and DCE intersect: M<ACE=90

( with a <---> above ACB and DCE)

9.)a=b and c=d : then a-c = b-d B

 

 

COLUMN 2

 

A. symmetric axiom

b.substitution axiom

c.transitive

d.definition of congruence

e.definition of perpendicular

f.reflexive axiom

g.addition

h.subtraction

i.defintion of midpoint

Expert Answers
pohnpei397 eNotes educator| Certified Educator

I'll give this a shot, though Geometry was a long time ago.  If you want to, you can message me to talk about anything you think may be wrong.

First, I believe that #9 should be H instead of B.  The subtraction postulate says "If equal quantities are subtracted from equal quantities, the differences are equal."  That's what you have going on in #9.

For ones you didn't try:

#2: I -- because they are all collinear and the two segments are congruent.  S must be midway between R and T.

#3: B

#6: D

#7: G

#8: E -- if two lines cross and make a right angle, they're prependicular.

neela | Student

1) a=a is reflexive property.

2)R, ST. R is point collenear with the line ST and RS=ST implies S is the midpoint of RT

3)AB+BC=AC. The line segments AB and BC are  added to get the line segment AC.

4)If a=b, then b=a . Both a and b  are  symmetric

5)a=b, b=c, then a=c is the definition of transitive property.

6)m<1=m<2.Since angle 1 and angle2 are equal, have the congruent property.

7)M<1 + m<2 ; then 2m<1 = m<1 +m2. Substituted the M<1 by m<1 and m<2 bym2 .Then sunbstited  m2 by m<1.

8)ACB and DCE intersect: M<ACE=90

The line segment ACB and DCE intersect at the point C making an angle ACE =90 degree.

9)a=b and c=d : then a-c = b-d B.

a=b...................(1)

c=d...................(2)

If we subtract (2) from (1), we get: a-c= b-d.

Considering the above reasons, the matching is as follows:

Matching:

(1) f, (2) i,   (3)  g,   (4) a,   (5) c,   (6) d,   (7) b,   (8) e, and (9) h.