Geometry Postulates and Theorems for Proofs

Question 1

Segment Addition Postulate

Answer 1

If point B is between points A and C on a line, then AB + BC = AC

Question 2

If point B is between points A and C on a line, then AB + BC = AC

Answer 2

Segment Addition Postulate

Question 3

Angle Addition Postulate

Answer 3

If Point S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

Question 4

If Point S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR`

Answer 4

Angle Addition Postulate

Question 5

Pythagorean Theorem

Answer 5

a^2 + b^2 = c^2

Question 6

a^2 + b^2 = c^2

Answer 6

Pythagorean Theorem

Question 7

a=a (P.O.E)

Answer 7

Reflexive P.O.E

Question 8

Reflexive P.O.E

Answer 8

a=a (P.O.E)

Question 9

Symmetric P.O.E

Answer 9

if a=b, then b=a (P.O.E)

Question 10

if a=b, then b=a (P.O.E)

Answer 10

Symmetric P.O.E

Question 11

if a=b, and b=c, then a=c (P.O.E)

Answer 11

Transitive P.O.E

Question 12

Transitive P.O.E

Answer 12

if a=b, and b=c, then a=c (P.O.E)

Question 13

if a=b, then b can be used in place of a

Answer 13

Substitution P.O.E

Question 14

Substitution P.O.E

Answer 14

if a=b, then b can be used in place of a

Question 15

y+2 = 7
y = 5
what P.O.E was used?

Answer 15

Subtraction P.O.E

Question 16

Subtraction P.O.E

Answer 16

y+2 = 7
y = 5
what P.O.E was used?

Question 17

y-2 = 7
y = 9
what P.O.E was used?

Answer 17

Addition P.O.E

Question 18

Addition P.O.E

Answer 18

y-2 = 7
y = 9
what P.O.E was used?

Question 19

y/2 = 4
y = 8
what P.O.E was used?

Answer 19

Multiplication P.O.E

Question 20

Multiplication P.O.E

Answer 20

y/2 = 4
y = 8
what P.O.E was used?

Question 21

Division P.O.E

Answer 21

2y = 8
y = 4
What P.O.E was used?

Question 22

2y = 8
y = 4
What P.O.E was used?

Answer 22

Division P.O.E

Question 23

Theorem 1-5

Answer 23

If two angles are congruent AND supplementary angles, then each angle is a right angle

Question 24

If two angles are congruent AND supplementary angles, then each angle is a right angle

Answer 24

Theorem 1-5

Question 25

Vertical Angles Theorem

Answer 25

All vertical angles are congruent

Question 26

All vertical angles are congruent

Answer 26

Vertical Angles Theorem

Question 27

Congruent Supplements / Compliments Theorem

Answer 27

If two angles are supplementary / complementary to the same angle (ex. A ≅ B, B≅C, where B is the 'Same Angle' as described) then they [A and C] are congruent

Question 28

If two angles are supplementary / complementary to the same angle (ex. A ≅ B, B≅C, where B is the 'Same Angle' as described) then they [A and C] are congruent

Answer 28

Congruent Supplements / Compliments Theorem

Question 29

Right Angle Theorem

Answer 29

All right angles are congruent

Question 30

All right angles are congruent

Answer 30

Right Angle Theorem

Question 31

Linear Pair Theorem

Answer 31

Linear Pairs are supplementary

Question 32

Linear pairs are supplementary

Answer 32

Linear Pair Theorem

Question 33

Same Side Interior Angles Postulate

Answer 33

If two parallel lines are cut by a transversal, then the Same-Side Interior Angles are Supplementary

Question 34

If two parallel lines are cut by a transversal, then the Same-Side Interior Angles are Supplementary

Answer 34

Same Side Interior Angles Postulate

Question 35

Corresponding Angles Theorem

Answer 35

If two parallel lines are cut by a transversal, then the Corresponding Angles are Congruent

Question 36

If two parallel lines are cut by a transversal, then the Corresponding Angles are Congruent

Answer 36

Corresponding Angles Theorem

Question 37

Alternate Interior Angles Theorem

Answer 37

If two parallel lines are cut by a transversal, then the Alternate Interior Angles are Congruent

Question 38

If two parallel lines are cut by a transversal, then the Alternate Interior Angles are Congruent

Answer 38

Alternate Interior Angles Theorem

Question 39

Alternate Exterior Angles Theorem

Answer 39

If two parallel lines are cut by a transversal, the Alternate Exterior Angles are congruent

Question 40

If two parallel lines are cut by a transversal, the Alternate Exterior Angles are congruent

Answer 40

Alternate Exterior Angles Theorem