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Geometry & Trigonometry Congruence

S7.1 Proofs

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Geometry & Trigonometry

Congruence

Proofs Related to the following theorems: - Complements of the same angle are congruent - Supplements of the same angle are congruent - Complements of congruent angles are congruent - Supplements of congruent angles are congruent - Vertical angles are congruent

61 Terms

1

Reason 2

Definition of congruent angles

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2

Reason 5

Definition of complementary angles

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3

Reason 6

Definition of complementary angles

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4

Reason 7

Substitution

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5

Reason 8

Subtraction property of equality

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6

Reason 9

Definition of congruent angles

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7

Reason 2

Complements of the same angle are congruent

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8

Reason 3

Definition of congruent angles

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9

Reason 5

Definition of supplementary angles

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10

Reason 6

Substitution

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11

Reason 7

Definition of supplementary angles

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12

Reason 3

Definition of vertical angles

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13

Reason 4

Given

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14

Reason 5

Angles in a linear pair are supplementary

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15

Reason 6

Given

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16

Reason 7

Angles in a linear pair are supplementary

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17

Reason 8

Supplements of the same angle are congruent

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18

Reason 2

Definition of angle bisector

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19

Reason 3

Definition of congruent angles

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20

Reason 4

Definition of vertical angles

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21

Reason 5

Definition of congruent angles

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22

Reason 6

Transitive property

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23

Reason 7

Definition of congruent angles

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24

Reason 2

Given

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25

Reason 3

Definition of supplementary angles

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26

Reason 4

Supplements of the same angle are congruent

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27

Reason 5

Definition of isosceles triangle

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28

Reason 2

Definition of complementary angles

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29

Reason 3

Subtraction property of equality

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30

Reason 4

Property of the angle

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31

Reason 5

Property of equality

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32

Reason 6

Subtraction property of equality

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33

Reason 7

Definition of the acute angle

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34

Reason 3

Angles in a linear pair are supplementary

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35

Reason 4

Supplements of the same angle are congruent

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36

Reason 5

Definition of an isosceles triangle

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37

Reason 1

Given

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38

Reason 2

Linear pair

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39

Reason 3

Supplements of the same angle are congruent

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40

Reason 4

Substitution

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41

Reason 5

Addition property of equality

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42

Reason 6

Division property of equality

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43

Reason 1

Given

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44

Reason 2

Right angles are congruent

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45

Reason 3

Given

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46

Reason 4

Angles in a linear pair are supplementary

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47

Reason 5

Given

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48

Reason 6

Supplements of congruent angles are congruent

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49

Reason 7

Given

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50

Reason 8

ASA

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51

Reason 9

CPCTC

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52

Reason 1

Given

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53

Reason 2

Given

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54

Reason 3

Definition of vertical angles

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55

Reason 4

Vertically opposite angles are congruent

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56

Reason 5

SAS postulate

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57

Reason 6

Corresponding parts of congruent triangles are congruent

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58

Reason 1

Given

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59

Reason 2

Definition of a linear pair

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60

Reason 3

Angles in a linear pair are supplementary

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61

Reason 4

Supplements of same angle are congruent

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