Download Lesson 4-4 - Elgin Local Schools

Lesson 4-4
Proving Congruence –
SSS, SAS
Ohio Content Standards:
Ohio Content Standards:
Describe and apply the properties of
similar and congruent figures; and
justify conjectures involving similarity
and congruence.
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:
Use coordinate geometry to
represent and examine the properties
of geometric figures.
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:
Prove or disprove conjectures and
solve problems involving two- and
three-dimensional objects
represented within a coordinate
system.
Ohio Content Standards:
Analyze two-dimensional figures in a
coordinate plane; e.g., use slope and
distance formulas to show that a
quadrilateral is a parallelogram.
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.
Side-Side-Side Congruence
Side-Side-Side Congruence
If the sides of one triangle
are congruent to the sides
of a second triangle, then
the triangles are
congruent.
Write a two - column proof to prove that
FEG  HIG if EI  FH , FE  HI , and
G is the midpoint of both EI and FH .
F
I
G
E
H
Determine whether WDV  MLP. Explain.
D
P
V
W
L
M
Side-Angle-Side Congruence
Side-Angle-Side Congruence
If two sides and the included angle
of one triangle are congruent to
two sides and the included angle
of another triangle, then the
triangles are congruent.
Write a proof for the following:
R
S
Given : RQ TS
RQ  TS
Prove : QRT  STR
Q
T
Determine which postulate can be used to
prove that the triangles are congruent. If
it is not possible to prove that they are
congruent, write not possible.
Determine which postulate can be used to
prove that the triangles are congruent. If
it is not possible to prove that they are
congruent, write not possible.
Assignment:
Pgs. 204-206
10-18 evens,
22-25 all,
32-40 all