Identify the Property which supports each Conclusion
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Transcript of Identify the Property which supports each Conclusion
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Identify the Property which supports each
Conclusion
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IF
then
AB BC
BC AB
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Symmetric Property of Congruence
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A A
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Reflexive Property of Congruence
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IF
and
then
AB BC
BC CD
AB CD
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Transitive Property of Congruence
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180m A m B If
and90m B 90 180m A then
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Substitution Property of
Equality
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IF
AB = CD
Then
AB + BC = BC + CD
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Addition Property of Equality
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If AB + BC= CE
and CE = CD + DE
then
AB + BC = CD + DE
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Transitive Property of Equality
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If
AC = BD
then
BD = AC.
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Symmetric Property of
Equality
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If AB + AB = AC
then 2AB = AC.
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Distributive Property
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m B m B
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Reflexive Property of Equality
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If
2(AM)= 14
then
AM=7
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Division Property of Equality
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If
AB + BC = BC + CD
then
AB = CD.
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Subtraction Property of
Equality
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If
AB = 4
then
2(AB) = 8
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Multiplication Property of
Equality
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Let’s see if you remember a few oldies but goodies...
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If B is a point between A and C, then
AB + BC = AC
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The Segment Addition Postulate
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If Y is a point in the interior of
then
RST
m RSY m YST m RST
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Angle Addition Postulate
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IF M is the Midpoint
of
then
AB
.AM MB
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The Definition of Midpoint
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IF
bisects
then
AB
CADCAB BAD
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The Definition of an Angle Bisector
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If AB = CD
then
AB CD
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The Definition of Congruence
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If
then
is a right angle.
90m AA
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The Definition of Right Angle
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1
If
is a right angle, then the lines are perpendicular.
1
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The Definition of Perpendicular
lines.
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If
Then
A B
m A m B
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The Definition of Congruence
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And now a few new ones...
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If and are right angles,
then
A B
A B
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Theorem: All Right angles are congruent.
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1 2
If and are congruent, then lines m and n are perpendicular.
n
m
1 2
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Theorem: If 2 lines intersect to form congruent adjacent angles, then the lines are perpendicular.
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If and are complementary, and and are complementary, then
AA
B
C
B C
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Theorem: If 2 angles are complementary to the same angle, they are congruent to each other.
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1 2
Then 1 2 180m m
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The Linear Pair Postulate
(The angles in a linear pair are supplementary.)
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1 2Then
1 2
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Theorem:
Vertical Angles are congruent.
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The End