ch 4.3 pt2 complete.notebook
November 16, 2009
Statements
1.
Reasons
1. GIVEN
AB=CB
FD bisects AB
FE bisects CB
2. D is the midpoint of AB
E is the midpoint of CB
2. Definition of a line segment bisector
3. AD = AB
CE = BC
3. Definition of a midpoint
4.
AD = BC
4. Substitution
5.
AD = CE
5. Substitution
6.
AD≅CE
6. Definition of Congruence
Oct 31­8:33 AM
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ch 4.3 pt2 complete.notebook
November 16, 2009
Theorem: If 2 angles are supplements of the same angle, then they are congruent
(Supplements of the same angle are congruent.)
Theorem: If 2 angles are supplements of congruent angles, then they are congruent.
(Supplements of congruent angles are congruent.)
**You must make sure that you CALL the angles supplementary or complementary before using these Theorems**
Nov 16­10:33 AM
Definition: Linear Pair ­ a pair of angles that are adjacent and sum to a straight angle.
2
1
<1 and <2 are a linear pair of angles
PROVE
Theorem: GIVEN
If 2 angles are a linear pair, then they are supplementary. ** You must make sure that you call angles a linear pair before you jump to them being supplementary**
1.
<1 and <2 are a linear pair of angles
1. GIVEN
2.
m<1 + m<2 = 180
2. Definition of a linear pair 3. <1 and <2 are supplementary
3. Definition of Supplementary
Nov 16­10:36 AM
2
ch 4.3 pt2 complete.notebook
November 16, 2009
Theorem: If 2 lines intersect to form congruent adjacent angles, then the lines must be perpendicular.
Prove this using the fact that congruent adjacent angles are formed when an angle is bisected. Since you are bisecting a straight angle, you know that right angles will result and all right angles are congruent.
Nov 16­9:38 AM
Definition: Vertical Angles
­when 2 lines intersect, the opposite angles formed are vertical angles
5
1
3
4
6
1
6
5
2
2
3
4
Theorem: If two angles are vertical angles, then they are congruent.
(Vertical angles are congruent)
Given: ABC and DBE
Prove: <1≅<2
Nov 16­9:41 AM
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ch 4.3 pt2 complete.notebook
November 16, 2009
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ch 4.3 pt2 complete.notebook
November 16, 2009
Nov 13­10:13 AM
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ch 4.3 pt2 complete.notebook
November 16, 2009
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ch 4.3 pt2 complete.notebook
November 16, 2009
Nov 13­10:14 AM
Nov 13­10:14 AM
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ch 4.3 pt2 complete.notebook
November 16, 2009
Nov 13­10:14 AM
Nov 13­10:14 AM
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