Download - Lesson 4-3: SSS, SAS, ASA 1 Lesson 4-3 Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)
Lesson 4-3: SSS, SAS, ASA 1
Lesson 4-3
Proving Triangles Congruent
(SSS, SAS, ASA, AAS, HL)
Lesson 4-3: SSS, SAS, ASA 2
PostulatesSSS If the sides of one triangle are congruent to the sides of a
second triangle, then the triangles are congruent.
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.
A
B C
D
E F
Lesson 4-3: SSS, SAS, ASA 3
Included Angles & Sides
& .A is the included angle for AB AC
& .B is the included angle for BA BC
& .C is the included angle for CA CB
A
B C
Included Angle:
Included Side:& .AB is the included side for A B
& .BC is the included side for B C
& .AC is the included side for A C
** *
Lesson 4-3: SSS, SAS, ASA 4
PostulatesASAIf 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.
SAS 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.
A
B C
D
E F
A
B C
D
E F
Lesson 4-3: SSS, SAS, ASA 5
Steps for Proving Triangles Congruent
1. Mark the Given.
2. Mark … Reflexive Sides / Vertical Angles
3. Choose a Method. (SSS , SAS, ASA)
4. List the Parts … in the order of the method.
5. Fill in the Reasons … why you marked the parts.
6. Is there more?
Lesson 4-3: SSS, SAS, ASA 6
Problem 1 Given: AB CD BC DAProve: ABC CDA
Statements Reasons
Step 1: Mark the Given Step 2: Mark reflexive sidesStep 3: Choose a Method (SSS /SAS/ASA )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?
A B
D C
SSS
1. AB CD2. BC DA3. AC AC
Given
Given
Reflexive Property
SSS Postulate4. ABC CDA
Lesson 4-3: SSS, SAS, ASA 7
Problem 2 Step 1: Mark the Given Step 2: Mark vertical anglesStep 3: Choose a Method (SSS /SAS/ASA)Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?
SAS
Given
Given
Vertical Angles.
SAS Postulate
: ;
Pr :
Given AB CB EB DB
ove ABE CBD
E
C
D
AB
1. AB CB2. ABE CBD
3. EB DB4. ABE CBD
Statements Reasons
Lesson 4-3: SSS, SAS, ASA 8
Problem 3
Statements Reasons
Step 1: Mark the Given Step 2: Mark reflexive sidesStep 3: Choose a Method (SSS /SAS/ASA)Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?
ASA
Given
Given
Reflexive Postulate
ASA Postulate
: ;
Pr :
Given XWY ZWY XYW ZTW
ove WXY WZY
Z
W Y
X 1. XWY ZWY
2. WY WY3. XYW ZYW
4. WXY WZY
Lesson 4-4: AAS & HL Postulate 9
Theorem
AAS If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.
A
B C
D
E F
Lesson 4-4: AAS & HL Postulate 10
Postulate
HL If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
A
B C
D
E F
Lesson 4-4: AAS & HL Postulate 11
Problem 1
Statements Reasons
Step 1: Mark the Given Step 2: Mark vertical anglesStep 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?
AAS
Given
Given
Vertical Angle Thm
AAS Postulate
Given: A C BE BDProve: ABE CBD
E
C
D
AB
1. A C2. ABE CBD
3. BE BD
4. ABE CBD
Lesson 4-4: AAS & HL Postulate 12
Problem 2
3. AC AC2. AB AD
1. ,ABC ADCright s
Step 1: Mark the Given Step 2: Mark reflexive sidesStep 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?
HL
Given
Given
Reflexive Property
HL Postulate
Given: ABC, ADC right s AB ADProve: ABC ADC
CB D
A
4. ABC ADC
Statements Reasons