Download Congruent Triangle Overview

11/14/2016
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 ≅ ∠Z
Sides: 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
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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
SAS
Description:
If the sides of one triangle are
congruent to the sides of another
triangle, the triangles are congruent.
Description:
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:
Diagram:
ΔABC ≅ ΔEDF
ΔABC ≅ ΔEFD
Triangle Congruency Shortcuts:
ASA
AAS
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:
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 ≅ ΔFED
ΔABC ≅ ΔDFE
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Triangle Congruency Shortcuts:
LL
HL
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:
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 ≅ ΔDEF
ΔABC ≅ ΔDEF
Triangle Congruency Shortcuts:
LA
HA
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:
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 ≅ ΔDEF
ΔABC ≅ ΔFDE
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SAS
HL
Vertical Angles …
congruent
AAS
Shared side…
congruent
Not ≅
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SSS
AAS
Shared side…
congruent
Vertical Angles …
congruent
Alternate Interior
Angles…
congruent
Not ≅
ASA
Shared side…
congruent
Alternate Interior
Angles…
congruent
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Not ≅
HL
SAS
AAS
Shared side…
congruent
Alternate Interior
Angles…
congruent
Shared side…
or in this case it’s
a hypotenuse…
congruent
Alternate Interior
Angles…
congruent
Shared side…
congruent
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SSS
Shared side…
congruent
Midpoints cut
things in half…
congruent
SAS
Shared side…
congruent
Alternate Interior
Angles…
congruent
Not ≅
ASA or AAS
Vertical Angles …
congruent
Alternate Interior
Angles…
congruent
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Shared side…
congruent
ASA
SAS
Bisecting…cutting
angles in
half…both sets…
congruent
Corresponding
angles…
congruent
HL
Shared side…Leg
in this case…
congruent
Not ≅
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Not ≅
AAS
SSS
AAS
Shared side…
congruent
Vertical Angles …
congruent
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