Transcript Geometry - San Ramon Valley High School

Geometry
Chapter 6 Review
Classify each statement as true or false.
1) If a > b and c> d, then a + b > c + d.
FALSE
2) If B is on AC, then AB + BC > AC.
FALSE
3) If x > y and y> 0, then xy> 0
TRUE
4) If S is in the interior of PQR, then mPQR > mSQR
TRUE
Suppose you plan to write an indirect proof of the statement:
If n > 10, then 2n + 3 > 23.
Write the correct first sentence of the indirect proof.
Assume temp. that 2n+3 < 23
Indirect Proof:
Given: 5x + 5 = 25
Prove: x = 3
Assume temp that x = 3, then 5x + 5 = 5(3) + 5 = 20
But this contradicts the given that 5x + 5 = 25.
Thus our assumption is false,
Therefore x does not equal 3.
Complete each statement by writing <, =, or >.
<
1) If mF > mG, then FH
H
HG.
2
2) If m 3 > m4, then FH
>
1
2
3
4
HG.
F
J
3) If FH < HG, then m1
>
m2.
G
In rectangle RECT, the diagonals intersect at M, mRMT = 88,
and mRME = 92. Which is longer, RE or RT? __________________________
RE
In triangle RST, m1 > m
R or T
.
>
In triangle RST, if RT < RS, then mT
In triangle RST, if mTSR < mR, then RT
mTSR
<
ST.
T
1
S
R
If RS = 15 and ST = 12, then the length of RT must be
greater than
and less than
.
3;27
If m1 = 135 and mR = 60, then the longest side of triangle
RST is _________________________________.
RS
Complete the statements by writing <,=, or >.
B
15
E
12
40 42
14
1
2
58
A 60
1) AB
<
AC
C
D
G
2) DG
<
F
12
>
GF
3) m1
m2
What can you deduce? Name the theorem.
F
18
G
88
E
92
18
EF>ED by SAS Ineq. Thm
D
t
a
1
2
b
Complete the indirect proof
Given: Transversal t cuts lines a and b; a is not parallel to b
Prove: 1 and 2 are not supplementary
Proof
Angles 1 and 2 are supp.
Assume temporarily that 1) ________________________________.
a//b.
Then 2)_____________________
since if two lines are cut by a transversal and same-side
interior angles are supplementary the lines are parallel.
But this contradicts the given information that 3) a is not // to b.
.
Angles 1 and 2 are supp.
Therefore the temporary assumption that 4) _______________________________
must be
false.
Angles 1 and 2 are not supp.
Therefore 5) __________________________________________________________.
Fill in the blanks.
24.
Given: AB > CD
Prove: AC > BD
A
Statements
B
C
Reasons
AB > CD
GIVEN
1) BC = BC
REFLEXIVE PROPERTY
2) AB + BC > BC + CD
A PROPERTY OF INEQUALITY
AB + BC = AC;
BC + CD = BD
3) SEGMENT ADDITION POSTULATE
AC > BD
4) SUBSTITUTION
D
HW
• Chapter Review P.235 #1-18
Check your odd answers
Look at Powerpoints to study