Download Lesson 4-6 Isosceles Triangles Ohio Content

Lesson 4-6
Isosceles Triangles
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:
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, test and establish the validity of
conjectures about geometric properties and
relationships using counterexample,
inductive and deductive reasoning, and
paragraph or two-column proof.
Vertex Angle
Vertex Angle
Angle formed by the congruent
sides in an isosceles triangle.
Vertex Angle
Angle formed by the congruent
sides in an isosceles triangle.
Vertex Angle
leg
leg
base
Base Angles
Base Angles
The two angles formed by the base
and one of the congruent sides.
Base Angles
The two angles formed by the base
and one of the congruent sides.
leg
leg
Base Angles
base
Theorem 4.9
Isosceles Triangle Theorem
Theorem 4.9
Isosceles Triangle Theorem
If two sides of a triangle are
congruent, then the angles opposite
those sides are congruent.
If DE  CD, BC  AC , and mCDE  120,
what is the measure of BAC ?
D
C
B
A
E
Theorem 4.10
Theorem 4.10
If two angles of a triangle are
congruent, then the sides opposite
those angles are congruent.
M
P
L
N
Name two congruent angles.
M
P
L
N
Name two congruent
segments.
Corollary 4.3
Corollary 4.3
A triangle is equilateral if it is
equiangular.
Corollary 4.4
Corollary 4.4
Each angle of an equilateral
triangle measures 60°.
E
F
H
J
G
In the figure, EJ bisects Ð2 and J lies on FG.
E
F
H
J
G
Find mHEJ and mEJH.
E
F
H
J
G
Find mEJG.
Assignment:
Pgs. 219-221
10-14 evens,
15-28 all,
44-46 evens