Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

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 SideThe side of a triangle that

is between two angles.

Postulate 4.3

Postulate 4.3

Angle-Side-Angle Congruence

Postulate 4.3

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.

Angle-Side-Angle Congruence

Write a proof.

Write a proof.

EDLWRL

EDWR

WEL

:Prove

. ofmidpoint theis :Given

R

W

LE

D

Theorem 4.5

Theorem 4.5

Angle-Angle-Side Congruence

Theorem 4.5

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.

Angle-Angle-Side Congruence

Write a proof.

Write a proof.

MNLN

JMKL

NJMNKL

:Prove

:Given

KJ

L

N

M

Assignment:

Pgs. 211-213 10-18 evens,

36-41 all