lesson 4-5 proving congruence – asa, aas. ohio content standards:

Lesson 4-5 Proving Congruence – ASA, AAS

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Lesson 4-5

Proving Congruence – ASA, AAS

Ohio Content Standards:

Describe and apply the properties of similar and congruent figures; and justify conjectures involving

similarity and congruence.

Page 4: Lesson 4-5 Proving Congruence – ASA, AAS. 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.

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

Ohio Content Standards:Use coordinate geometry to

represent and examine the properties of geometric figures.

Page 6: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Ohio Content Standards:Prove or disprove conjectures and solve problems involving two- and

three-dimensional objects represented within a coordinate

system.

Page 7: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

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.

Page 8: Lesson 4-5 Proving Congruence – ASA, AAS. 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.

Page 9: Lesson 4-5 Proving Congruence – ASA, AAS. 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.

Page 10: Lesson 4-5 Proving Congruence – ASA, AAS. 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.

Page 11: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Included Side

Page 12: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Included SideThe side of a triangle that

is between two angles.

Page 13: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Postulate 4.3

Page 14: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Postulate 4.3

Angle-Side-Angle Congruence

Page 15: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

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

Page 16: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Write a proof.

Page 17: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Write a proof.

EDLWRL

EDWR

WEL

:Prove

. ofmidpoint theis :Given

Page 18: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Theorem 4.5

Page 19: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Theorem 4.5

Angle-Angle-Side Congruence

Page 20: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

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

Page 21: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Write a proof.

Page 22: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Write a proof.

MNLN

JMKL

NJMNKL

:Prove

:Given

Page 23: Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Assignment:

Pgs. 211-213 10-18 evens,

36-41 all

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