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Title: Congruent Triangles
Objective: Students will be able to identify congruent triangles when given few measurements.
Language Objective: Students will be able to describe the different types of triangle congruency.
Essential Question: “Why is knowing about triangle congruency important?”
Congruent Triangle Overview:CPCTC: Corresponding Parts of Congruent Triangles are Congruent
Congruency Statement: ΔABC ≅ ΔXYZ (Note: Order of symbols and letters matters)
Congruent Corresponding Parts:Angles: ∠A ≅ ∠X ∠B ≅ ∠Y ∠C ≅ ∠ZSides: AB ≅ XY BC ≅ YZ AC ≅ XZ
(Note: Use the Congruency Statement)
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Congruent Triangle Overview:Problem solving:
ΔDEF ≅ ΔMNP. Calculate the values of x, y, and m∠D
For x:
5x + 10 = 60
-10 -10
5x = 50
5 5
x = 10
Congruent Triangle Overview:Problem solving:
ΔDEF ≅ ΔMNP. Calculate the values of x, y, and m∠D
Length of side NP:
NP = 4(10) – 12 = 28
11/14/2016
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Congruent Triangle Overview:Problem solving:
ΔDEF ≅ ΔMNP. Calculate the values of x, y, and m∠D
For y:
4y + 4 = 28
-4 -4
4y = 24
4 4
y = 6
Congruent Triangle Overview:Problem solving:
ΔDEF ≅ ΔMNP. Calculate the values of x, y, and m∠D
For m∠D:
m∠D = 5(6) = 30°
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Triangle Congruency Shortcuts:SSS
Description:
If the sides of one triangle are congruent to the sides of another triangle, the triangles are congruent.
Diagram:
SASDescription:
If two sides and the included angle of one triangle are congruent to the two sides and included angle of another triangle, the triangles are congruent.
Diagram:
ΔABC ≅ ΔEFDΔABC ≅ ΔEDF
Triangle Congruency Shortcuts:ASA
Description:
If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, the triangles are congruent.
Diagram:
AAS
Description:
If two angles and the non-included side of one triangle are congruent to the two angles and non-included side of another triangle, the triangles are congruent.
Diagram:
ΔABC ≅ ΔFEDΔABC ≅ ΔDFE
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Triangle Congruency Shortcuts:LL
Description:
In a right triangle, if the legs of one triangle are congruent to the corresponding legs of another triangle, the triangles are congruent.
Diagram:
HL
Description:
In a right triangle, if the hypotenuse and the leg of one triangle are congruent to the hypotenuse and corresponding leg of another triangle, the triangles are congruent.
Diagram:
ΔABC ≅ ΔDEFΔABC ≅ ΔDEF
Triangle Congruency Shortcuts:LA
Description:
In a right triangle, if one acute angle and leg of one triangle are congruent to the corresponding acute angle and corresponding leg of another triangle, the triangles are congruent.
Diagram:
HA
Description:
In a right triangle, if the hypotenuse and one acute angle of the triangle are congruent to the corresponding hypotenuse and acute angle of another triangle, the triangles are congruent.
Diagram:
ΔABC ≅ ΔDEFΔABC ≅ ΔFDE
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SAS AASVertical Angles … congruent
Shared side…congruent
HL Not ≅
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AASSSSShared side…congruent
Vertical Angles … congruent
Not ≅ ASA Shared side…congruent
Alternate Interior Angles…congruent
Alternate Interior Angles…congruent
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Not ≅ HL Shared side…or in this case it’s a hypotenuse…congruent
SAS AASShared side…congruent
Alternate Interior Angles…congruent
Shared side…congruentAlternate Interior
Angles…congruent
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SASSSSMidpoints cut things in half…congruentShared side…
congruent
Shared side…congruent
Not ≅ASA or AASAlternate Interior Angles…congruent
Alternate Interior Angles…congruent
Vertical Angles … congruent
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HLASA Bisecting…cutting angles in half…both sets…congruent
Shared side…congruent
Shared side…Leg in this case…congruent
Not ≅SASCorresponding angles…congruent
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Not ≅ AASShared side…congruent
AASSSSVertical Angles … congruent
