Download Lesson 4-5 Proving Congruence

Lesson 4-5
Proving Congruence –
ASA, AAS
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
two-dimensional figures and
three-dimensional objects.
Ohio Content Standards:
Use coordinate geometry to
represent and examine the
properties of geometric figures.
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
two-dimensional figures and
three-dimensional 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.
Included Side
Included Side
The side of a triangle that
is between two angles.
Postulate
4.3
Postulate
4.3
Angle-Side-Angle Congruence
Postulate
4.3
Angle-Side-Angle Congruence
If two angles and the included
side of one triangle are
congruent to two angles and the
included side of another triangle,
then the triangles are congruent.
Write a proof.
Write a proof.
Given : L is the midpoint of WE.
WR ED
Prove :
WRL 
EDL
R
E
L
W
D
Theorem
4.5
Theorem
4.5
Angle-Angle-Side Congruence
Theorem
4.5
Angle-Angle-Side Congruence
If two angles and the
nonincluded side of one triangle
are congruent to the
corresponding two angles and
side of a second triangle, then
the two triangles are congruent.
Write a proof.
Write a proof.
Given : NKL  NJM
KL  JM
Prove : LN  MN
K
J
L
M
N
Assignment:
Pgs. 211-213
10-18 evens,
36-41 all