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Title: Q4 Math8 PROVING TRIANGLE CONGRUENCE
Description: COMPLETE NOTES OF PROVING TRIANGLE CONGRUENCE FOR QUARTER 4 MATH8
Description: COMPLETE NOTES OF PROVING TRIANGLE CONGRUENCE FOR QUARTER 4 MATH8
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ST
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PHOENIX Math for the 21st Century Learners: Second Edition, PHOENIX Publishing House Inc
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Prove two triangles are congruent applying the triangle congruence postulates
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These can now be used to prove the congruence of triangles using deductive reasoning
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π΅
EXAMPLE 1: Given: Μ Μ Μ Μ
π΄π΅ β Μ Μ Μ Μ
π΄π·, Μ Μ Μ Μ
π΅πΆ β Μ Μ Μ Μ
π·πΆ
Prove: βπ΄π΅πΆ β βπ΄π·πΆ
πΆ
Proof:
STATEMENT
Μ Μ Μ Μ β π¨π«
Μ Μ Μ Μ
1
...
π©πͺ
Μ Μ Μ Μ β π¨πͺ
Μ Μ Μ Μ
3
...
βπ΄π΅πΆ β βπ΄π·πΆ
π΄
REASONS
1
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Given
3
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SSS Postulate
π·
The ππ΄π Congruence Postulate states that if two sides and the included angle of one triangle are congruent to two
sides and the included angle of another triangle, then the triangles are congruent
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EXAMPLE 2: Given: Μ Μ Μ Μ
π΄π΅ β Μ Μ Μ Μ
πΆπ·, Μ Μ Μ Μ
π΄π΅ β₯ π΅π·
πΆπ· β₯ Μ Μ Μ Μ
π΅π·, πΈ is the midpoint of π΅π·
Prove: βABE β βCDE
π΄
π΅
Proof:
πΆ
πΈ
π·
STATEMENT
Μ Μ Μ Μ β πͺπ«
Μ Μ Μ Μ
1
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β π΅ is a right angle
Μ Μ Μ Μ β₯ π΅π·
Μ Μ Μ Μ
3
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βπ΄π΅πΆ β βπ΄π·πΆ
5
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Μ Μ Μ Μ and π΅πΈ
Μ Μ Μ Μ
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πΆπ·
Μ Μ Μ Μ Μ
6
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7
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βABE β βCDE
REASONS
1
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Definition of Perpendicular
3
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Definition of Perpendicular
5
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6
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Definition of midpoint
8
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π΄
EXAMPLE 3: Given: β 1 β β 2, π· is the midpoint of Μ Μ Μ Μ
π΅πΆ
...
1
2
Prove: βπ΄π·π΅ β βπ΄π·πΆ
π΅
Proof:
STATEMENT
π·
πΆ
REASONS
1
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β π΄π΅π· and β 1 form a linear pair
β π΄πΆπ· and β 2 form a linear pair
3
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β π¨π©π« β β π¨πͺπ«
5
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1
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Μ Μ Μ Μ Μ
π©π« β Μ Μ Μ Μ
πͺπ«
7
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β π΄π·πΆ is a right angle
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β π¨π«π© β β π¨π«πͺ
6
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βπ΄π·π΅ β βπ΄π·πΆ
9
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Definition of a linear pair
3
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Supplements to congruent angles are congruent
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Given
7
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Any two right angles are congruent
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KINDLE YOUR IDEAS
ACTIVITY
Direction: Complete each proof
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CHOICES:
β’ Any two right angles are congruent
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Given:
Prove:
Proof:
Μ Μ Μ Μ β Μ Μ Μ Μ
π΄πΆ
π·πΈ
Μ Μ Μ Μ β₯ πΆπ΅
Μ Μ Μ Μ , π·πΈ
Μ Μ Μ Μ β₯ πΈπ΅
Μ Μ Μ Μ
π΄πΆ
Μ Μ Μ Μ β πΈπ΅
Μ Μ Μ Μ
πΆπ΅
βπ΄πΆπ΅ β βπ·πΈπ΅
STATEMENT
Μ Μ Μ Μ β π·πΈ
Μ Μ Μ Μ
1
...
π΄πΆ
3
...
π΅
π΄
π·
REASONS
1
...
3
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β πΆ β β πΈ
5
...
6
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CHOICES:
β’ Alternate-Interior Angles are equal
β’ Given
β’ Definition of Vertical Angles
Μ Μ Μ Μ
β’ Μ Μ Μ Μ
π΄π΅||π·πΈ
β’ Angle-Side-Angle Postulate
β’ βπ΄π΅πΆ β βπ·πΈπΆ
πΈ
5
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Given:
Prove:
Proof:
π΅
STATEMENT
π·
REASONS
1
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Given
Μ Μ Μ Μ β Μ Μ Μ Μ
2
...
3
...
4
...
5
...
πΆ
π΄
πΈ
ADDITIONAL NOTES TO REVIEW:
SPECIAL RIGHT TRIANGLES
In a right triangle, if one angle measures 30Λ, the length of the hypotenuse is twice the length of the side
opposite the angle with measure 30Λ
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If one angle of a right triangle measures 30Λ, the length of the side opposite the angle with measure 60Λ is
equal toβπ times the length of the side opposite the 30Λ angle
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4π₯ + 6
8π₯ β 18
Solve for the value of x
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Then transpose to combine similar terms, 6 + 18 = 8π₯ β 4π₯
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24 4π₯
=
4
4
6=π₯
,
Title: Q4 Math8 PROVING TRIANGLE CONGRUENCE
Description: COMPLETE NOTES OF PROVING TRIANGLE CONGRUENCE FOR QUARTER 4 MATH8
Description: COMPLETE NOTES OF PROVING TRIANGLE CONGRUENCE FOR QUARTER 4 MATH8