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Congruent Figures
February 23, 2012
Section 4-1 Congruent Figures
 Objectives: Today you will learn to
 Recognize congruent figures and identify
corresponding parts
Which figures are congruent?
Congruent
Not Congruent
Definition Congruent Polygons
Polygons are congruent when they have
congruent corresponding sides and
congruent corresponding angles
Definition Congruent Triangles
Two triangles are congruent when they
have three pairs of congruent
corresponding sides and three pairs
of congruent corresponding angles
Congruent Triangles
ΔABC ≅ ΔDEF – Congruency Statement
Order Matters! ΔABC ΔEFD
Congruent Triangles
ΔABC ≅ ΔDEF
Name Congruent Parts
AB
Congruent Triangles
Name Congruent
Parts
ΔABC ≅ ΔDEF
Angles:
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Lines:
Congruent Triangles
Example 1:
ΔLMN ≅ ΔRST
List Corresponding Congruent Parts:
Congruent Triangles
Example 1
ΔLMN ≅ ΔRST
Name Congruent Parts:
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Congruent Triangles: Proof
Example 2:
Prove ΔABC ≅ ΔEDC
Theorem 4-1
If two angles of one triangle are
congruent to two angles of another
triangle, then the third angles are
congruent.
∠C ≅ ∠F
Theorem
If two angles of one triangle are
congruent to two angles of another
triangle, then the third angles are
congruent.
∠C ≅ ∠F
Why???
Theorem
If m∠A + m∠B + m∠C = 1800
and m∠D + m∠E + m∠F = 1800
}
Triangle Angle-Sum Thm
Theorem
If m∠A + m∠B + m∠C = 1800
and m∠D + m∠E + m∠F = 1800
then m∠A + m∠B + m∠C =
m∠D + m∠E + m∠F
}
Triangle Angle-Sum Thm
Theorem
If m∠A + m∠B + m∠C = 1800
and m∠D + m∠E + m∠F = 1800
then m∠A + m∠B + m∠C =
m∠D + m∠E + m∠F
Since m∠A= m∠D and
m∠B= m∠E then
}
Triangle Angle-Sum Thm
Theorem
If m∠A + m∠B + m∠C = 1800
and m∠D + m∠E + m∠F = 1800
then m∠A + m∠B + m∠C =
m∠D + m∠E + m∠F
Since m∠A= m∠D and
m∠B= m∠E then
m∠C = m∠F
=>∠C ≅ ∠F
}
Triangle Angle-Sum Thm
Note: This is ANGLE congruence, not triangle congruence
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 3
Prove ΔADB ≅ ΔADC
Congruent Triangles: Proof
Example 4:
Can you Prove
ΔLNM ≅ ΔPON?
Congruent Triangles: Proof
Example 5:
Prove: ΔABD ≅ ΔCBD
Given:
Congruent Triangles: Proof
Example 5:
Prove: ΔABD ≅ ΔCBD
Given:
Proof:
1.
1. Given
2.
3.
2. Reflexive
3. If 2 ∠’s are ≅
then the 3rd∠’s
are ≅
4. Def of ≅ Δ’s
4. ΔABD ≅ ΔCBD
Congruent Triangles
Example 6: Given ΔABC ≅ ΔDEF
Find m∠F
∠A ≅ ∠D
m∠D = 46
100+46+ m∠F =180
m∠F = 180 – 146
m∠F = 34
Congruent Figures
Example 7:
Given EFGH ≅ JKLM
m∠E = 730
m∠G = 560
m∠K = 1120
Find m∠M
Congruent Figures
Example 7:
Given EFGH ≅ JKLM
m∠E = 730
m∠G = 560
m∠K = 1120
m∠J+ m∠K+ m∠L+ m∠M =
360 [(n-2)*180]
Find m∠M
73 +112+ 56+ m∠M = 360
m∠M = 119
m∠E = m∠J = 730
m∠G = m∠L = 560
Congruent Figures
Example 7:
Given EFGH ≅ JKLM
m∠E = 730
m∠G = 560
m∠K = 1120
m∠J+ m∠K+ m∠L+ m∠M =
360 [(n-2)*180]
Find m∠M
73 +112+ 56+ m∠M = 360
m∠M = 119
m∠E = m∠J = 730
m∠G = m∠L = 560
Congruent Figures
Example 7:
Given EFGH ≅ JKLM
m∠E = 730
m∠G = 560
m∠K = 1120
m∠J+ m∠K+ m∠L+ m∠M =
360 [(n-2)*180]
Find m∠M
73 +112+ 56+ m∠M = 360
m∠M = 119
m∠E = m∠J = 730
m∠G = m∠L = 560
Congruent Figures
Example 7:
Given EFGH ≅ JKLM
m∠E = 730
m∠G = 560
m∠K = 1120
m∠J+ m∠K+ m∠L+ m∠M =
360 [(n-2)*180]
Find m∠M
73 +112+ 56+ m∠M = 360
m∠M = 119
m∠E = m∠J = 730
m∠G = m∠L = 560
Wrap-up
 Today you learned to recognize
congruent figures and identify
corresponding parts
 Tomorrow you’ll learn how to prove
triangles congruent using the SSS
and SAS Postulates
Homework:
pp. 182 – 184: 3-28, 30-35, 38-40, 44