Lesson 4-6Lesson 4-6

Isosceles TrianglesIsosceles Triangles

Ohio Content Standards:Ohio Content Standards:

Ohio Content Standards:Ohio Content Standards:Describe and apply the properties Describe and apply the properties of similar and congruent figures; of similar and congruent figures; and justify conjectures involving and justify conjectures involving

similarity and congruence.similarity and congruence.

Ohio Content Standards: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: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: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 AngleVertex Angle

Vertex AngleVertex AngleAngle formed by the congruent Angle formed by the congruent sides in an isosceles triangle.sides in an isosceles triangle.

Vertex AngleVertex AngleAngle formed by the congruent Angle formed by the congruent sides in an isosceles triangle.sides in an isosceles triangle.

Vertex Anglelegleg

base

Base AnglesBase Angles

Base AnglesBase AnglesThe two angles formed by the base The two angles formed by the base

and one of the congruent sides.and one of the congruent sides.

Base AnglesBase AnglesThe two angles formed by the base The two angles formed by the base

and one of the congruent sides.and one of the congruent sides.

Base Angleslegleg

base

Theorem 4.9Theorem 4.9Isosceles Triangle TheoremIsosceles Triangle Theorem

Theorem 4.9Theorem 4.9Isosceles Triangle TheoremIsosceles Triangle Theorem

If two sides of a triangle are If two sides of a triangle are congruent, then the angles opposite congruent, then the angles opposite

those sides are congruent.those sides are congruent.

? of measure theiswhat ,120 and, , If

BACCDEmACBCCDDE

A

B C

D

E

Theorem 4.10Theorem 4.10

Theorem 4.10Theorem 4.10

If two angles of a triangle are If two angles of a triangle are congruent, then the sides opposite congruent, then the sides opposite

those angles are congruent.those angles are congruent.

L

P

Name two congruent angles.

M

N

L

P

Name two congruent segments.

M

N

Corollary 4.3Corollary 4.3

Corollary 4.3Corollary 4.3

A triangle is equilateral if it is A triangle is equilateral if it is equiangular.equiangular.

Corollary 4.4Corollary 4.4

Corollary 4.4Corollary 4.4

Each angle of an equilateral Each angle of an equilateral triangle measures 60triangle measures 60°.°.

E

HF GJ

E

HF GJ

. and Find EJHmHEJm

E

HF GJ

. Find EJGm

Assignment:Assignment:

Pgs. 219-221 Pgs. 219-221 10-14 evens,10-14 evens,

15-28 all, 15-28 all, 44-46 evens44-46 evens