Proving triangles congruent
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Proving Triangles Congruent. Lesson 4-3. (SSS, SAS, ASA). A. D. F. B. C. E. Postulates. If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. SSS. Included Angle:.

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Proving triangles congruent

Proving Triangles Congruent

Lesson 4-3

(SSS, SAS, ASA)

Lesson 4-3: SSS, SAS, ASA


Postulates

A

D

F

B

C

E

Postulates

If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

SSS

Included Angle:

In a triangle, the angle formed by two sides is the included angle for the two sides.

Included Side:

The side of a triangle that forms a side of two given angles.

Lesson 4-3: SSS, SAS, ASA


Included angles sides
Included Angles & Sides

Included Angle:

*

*

*

Included Side:

Lesson 4-3: SSS, SAS, ASA


Postulates1

A

A

D

D

B

C

B

C

F

F

E

E

Postulates

If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent.

ASA

If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.

SAS

Lesson 4-3: SSS, SAS, ASA


Steps for Proving Triangles Congruent

  • Mark the Given.

  • Mark … Reflexive Sides/Vertical Angles

  • Choose a Method. (SSS , SAS, ASA)

  • List the Parts … in the order of the method.

  • Fill in the Reasons … why you marked the parts.

  • Is there more?

Lesson 4-3: SSS, SAS, ASA


Problem 1

A

B

@

AB

CD

1.

@

BC

DA

2.

@

AC

CA

3.

C

D

Problem 1 

Step 1: Mark the Given

Step 2: Mark reflexive sides

SSS

Step 3: Choose a Method (SSS /SAS/ASA )

Step 4: List the Parts in the order of the method

Step 5: Fill in the reasons

Step 6: Is there more?

Given

Given

Reflexive Property

SSS Postulate

Lesson 4-3: SSS, SAS, ASA


Problem 2
Problem 2

Step 1: Mark the Given

Step 2: Mark vertical angles

SAS

Step 3: Choose a Method (SSS /SAS/ASA)

Step 4: List the Parts in the order of the method

Step 5: Fill in the reasons

Step 6: Is there more?

Given

Vertical Angles.

Given

SAS Postulate

Lesson 4-3: SSS, SAS, ASA


Problem 3

X

W

Y

Z

Problem 3

Step 1: Mark the Given

Step 2: Mark reflexive sides

ASA

Step 3: Choose a Method (SSS /SAS/ASA)

Step 4: List the Parts in the order of the method

Step 5: Fill in the reasons

Step 6: Is there more?

Given

Reflexive Postulate

Given

ASA Postulate

Lesson 4-3: SSS, SAS, ASA


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