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Triangle Congruence (SSS, SAS, ASA, AAS, HL)
Presentation
•
Mathematics
•
8th - 10th Grade
•
Medium
Standards-aligned
Angela Preston
Used 26+ times
FREE Resource
46 Slides • 22 Questions
1
Triangle Congruence (SSS, SAS, ASA, AAS, HL)
by Angela Preston
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The Idea of Congruence
Two geometric figures with exactly the same size and shape.
3
4
Corresponding Parts
In a previous lesson, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent
5
Match
Match the congruent parts
Angle A
EF
FE
∠B
∠F
Angle D
Angle D
BC
CB
∠E
∠C
6
Corresponding Parts
Congruence statements are written such that the corresponding, congruent parts are listed in the same order.
In this figure, the following congruence statements are also true:
Δ BCA ≅ Δ EFD
Δ ACB ≅ Δ DFE
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Multiple Choice
If ∆LMK ≅ ∆LMT, then ∠K ≅ ____
MT
∠T
∠M
∠L
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Multiple Choice
Choose the correct congruence statement for the figures shown.
∆TUV ≅ ∆EUV
∆VUT ≅ ∆UVE
∆TUV ≅ ∆UEV
∆UTV ≅ ∆EUV
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Do you need to show that all six parts are congruent???
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Triangle Congruence Shortcuts
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Side-Side-Side (SSS)
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
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Side-Side-Side (SSS)
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
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Side-Side-Side (SSS)
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
Label the sides of the first triangle on your paper to illustrate SSS!
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Multiple Choice
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What is an Included Angle?
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Name the Included Angle...
***For this activity, complete problem #2 on your paper!
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Name the Included Angle...
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Name the Included Angle...
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Name the Included Angle...
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Side-Angle-Side (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.
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Side-Angle-Side (SAS)
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Side-Angle-Side (SAS)
Label the sides of the second triangle on your paper to illustrate SAS!
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Multiple Choice
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What is an Included Side?
The side between two angles
This combo is called angle-side-angle, or just ASA.
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Name the Included Side...
***For this activity, complete problem #3 on your paper!
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Name the Included Side...
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Name the Included Side...
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Name the Included Side...
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Angle-Side-Angle (ASA)
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.
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Angle-Side-Angle (ASA)
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Angle-Side-Angle (ASA)
Label the sides of the third triangle on your paper to illustrate ASA!
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Multiple Choice
Which triangle congruence theorem can be used to prove the triangles are congruent?
AAA
SSS
ASA
N/A
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Angle-Angle-Side (AAS)
If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent.
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Angle-Angle-Side (AAS)
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Angle-Angle-Side (AAS)
Label the sides of the fourth triangle on your paper to illustrate AAS!
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What other congruence statements can I write?
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What other congruence statements can I write?
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Multiple Choice
Which triangle congruence theorem can be used to prove the triangles are congruent?
AAS
AAA
SAS
SSS
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Warning: No SSA Postulate
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Warning: No SSA Postulate
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BUT: SSA DOES work in one situation!
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WE CALL THIS...
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Hypotenuse-Leg (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
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Hypotenuse-Leg (HL)
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Hypotenuse-Leg (HL)
Label the sides of the fifth triangle on your paper to illustrate HL!
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Multiple Choice
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
ASA
SSA
HL
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Multiple Choice
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Warning: No AAA Postulate
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Congruence Postulates and Theorems
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Multiple Choice
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Multiple Choice
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
ASA
AAS
NOT ENOUGH INFORMATION!
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Multiple Choice
Name the postulate, if possible, that makes the triangles congruent.
SAS
AAS
ASA
NOT ENOUGH INFORMATION!
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Multiple Choice
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Multiple Choice
Name the postulate, if possible, that makes the triangles congruent.
SSS
ASA
AAS
NOT ENOUGH INFORMATION!
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Vertical Angles, Reflexive Sides and Angles
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Let’s Practice...
Indicate the additional information needed to enable us to apply the specified congruence postulate. This activity coincides with problem #5 on your paper!
For ASA:
For SAS:
For AAS:
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Let’s Practice...
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Let’s Practice...
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Let’s Practice...
60
Multiple Choice
61
Multiple Choice
Which postulate can we use to prove the two triangles are congruent?
SSS
SAS
ASA
AAS
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Multiple Choice
63
Multiple Choice
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Multiple Choice
65
Multiple Choice
66
Multiple Choice
67
Multiple Choice
SSS
SAS
AAS
Not Possible
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Class Assignment
Go to your online textbook (clever.com).
Complete the following assignment by the due date:
"Triangle Congruence"
Triangle Congruence (SSS, SAS, ASA, AAS, HL)
by Angela Preston
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