Download Lesson 2-7 Proving Segment Relationships

Lesson 2-7
Proving Segment
Relationships
Ohio Content Standards:
Ohio Content Standards:
Establish the validity of conjectures
about geometric objects, their
properties and relationships by
counter-example, inductive and
deductive reasoning, and critiquing
arguments made by others.
Ohio Content Standards:
Make and test conjectures about
characteristics and properties (e.g.,
sides, angles, symmetry) of twodimensional figures and threedimensional objects.
Ohio Content Standards:
Make, test and establish the validity of
conjectures about geometric
properties and relationships using
counterexample, inductive and
deductive reasoning, and paragraph
or two-column proof.
Postulate 2.8
Ruler Postulate
Postulate 2.8
Ruler Postulate
The points on any line or line
segment can be paired with real
numbers so that, given any two
points A and B on a line, A
corresponds to zero, and B
corresponds to a positive real
number.
Postulate 2.9
Segment Addition Postulate
Postulate 2.9
Segment Addition Postulate
If B is between A and C,
then AB + BC = AC.
Postulate 2.9
Segment Addition Postulate
If B is between A and C,
then AB + BC = AC.
If AB + BC = AC,
then B is between A and C.
Prove the following.
Given: PR = QS
Prove: PQ = RS
P
Q
R
S
Theorem 2.2
Segment Congruence
Theorem 2.2
Segment Congruence
Congruence of segments is reflexive,
symmetric, and transitive.
.
Theorem 2.2
Segment Congruence
Congruence of segments is reflexive,
symmetric, and transitive.
Reflexive Property
AB
.
AB
Theorem 2.2
Segment Congruence
Congruence of segments is reflexive,
symmetric, and transitive.
Symmetric Property
If AB CD, then CD AB.
.
Theorem 2.2
Segment Congruence
Congruence of segments is reflexive,
symmetric, and transitive.
Transitive Property
If AB  CD, and CD  EF,
then AB EF.
.
Prove the following.
3 cm
Given: WY = YZ
YZ  XZ
XZ  WX
Prove: WX  WY
Y
Z
3 cm
W
X
Assignment:
Pgs. 104 - 106
12-20 all,
32-44 evens