Proofs - Theorems And Postulates

Front 1

Segment Addition Postulate

Back 1

If Q is between P and R, then PQ + QR = PR

Hint 1

Front 2

Angle Addition Postulate

Back 2

If R is in the interior of <PQS, then m<PQS = m<PQR + m<RQS

Hint 2

Front 3

Reflexive Property

Back 3

For any number a, a=a

Hint 3

17 = 17

Front 4

Symmetric Property

Back 4

for any numbers a and b, if a=b, then b=a

Hint 4

17 = 1D
∴ 1D = 17

Front 5

Transitive Property

Back 5

for any numbers a, b, and c, if a=b and b=c, then a=c.

Hint 5

1D = 17
5B = 1D
∴ 5B = 17

Front 6

Addition Property of Equality

Back 6

if a=b, then a+c=b+a

Hint 6

1D = 17
1D + 3 = 17 + 3 (20)

Front 7

Subtraction Property of Equality

Back 7

if a=b, then a-c = b-c

Hint 7

1D = 17
1D - 3 = 17 - 3 (14)

Front 8

Multiplication Property of Equality

Back 8

if a=b, then a*c=b*c

Hint 8

1D = 17
1D * 3 = 17 * 3 (51)

Front 9

Division Property of Equality

Back 9

if a = b, then a/c = b/c

Hint 9

1D = 17
1D/3 = 17/3 (5.667)

Front 10

Substitution Property

Back 10

if a = b, then b can be substituted for a.

Hint 10

D = O
1D = 17
1O = 17

Front 11

Definition of...

Back 11

Use definitions when you are restating the same information in a new form.

Hint 11

M = midpoint of AB
∴ AM = MB (definition of midpoint)

Front 12

Linear Pair Postulate

Back 12

If two angles form a linear pair, then they are supplementary angles.

Hint 12

∴ m<1 + m<2 = 180

Front 13

Congruent Supplements Theorem

Back 13

Angles supplementary to the same angle are congruent.

Hint 13

∴ m<1 = m< 3

Front 14

Congruent Complements Theorem

Back 14

Angles complementary to the same angle are congruent.

Front 15

Vertical Angles Theorem

Back 15

Vertical angles are congruent.

Hint 15

Front 16

Corresponding Angles Postulate

Back 16

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

Hint 16

∴ m<1 = m<2

Front 17

Alternate Interior Angles Theorem

Back 17

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

Hint 17

(The angles that are 64 degrees are INTERIOR to lines KO and LN)

Front 18

Same Side (Consecutive) Interior Angles Theorem

Back 18

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

Hint 18

∴ <3 = <5
∴ <6 = <4

Front 19

Alternate Exterior Angles Theorem

Back 19

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

Hint 19

Front 20

Converse of Corresponding Angles Postulate

Back 20

If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

Hint 20

∴ l and m are parallel.

Front 21

Converse of Same-Side (Consecutive) Interior Angles Theorem

Back 21

If two lines in a place are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.

Front 22

Converse of Alternate Interior Angles Theorem

Back 22

If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.

Hint 22

∴ JC is parallel to KM

Front 23

Perpendicular Transversal Theorem

Back 23

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Hint 23

if T is perpendicular to K, and K is parallel to L, then T is perpendicular to L.

Front 24

Parallel Postulate

Back 24

If there is a line and a point not on the line, then there exists exactly on line through the point that is parallel to the given line.

Hint 24

Front 25

Triangle Sum Theorem

Back 25

The sum of the measures of the angles of a triangle is 180.

Hint 25

Front 26

Triangle Exterior Angle Theorem

Back 26

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Hint 26

Front 27

Third Angles Theorem

Back 27

If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent.

Front 28

Side-Side-Side Postulate

Back 28

If the sides of one triangle are congruent to the sides of another triangle, then the triangles are congruent.

Hint 28

∴ 🔺ABC ≅ 🔺DEF

Front 29

Side-Angle-Side Postulate

Back 29

If two sides and the angle included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Hint 29

∴ 🔺ABC ≅ 🔺DEF

Front 30

Angle-Side-Angle Postulate

Back 30

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Hint 30

∴ 🔺ABC ≅ 🔺DEF

Front 31

Angle-Angle-Side Postulate

Back 31

If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

Hint 31

∴ 🔺ABC ≅ 🔺DEF

Front 32

Corresponding Parts of Congruent Triangles Are Congruent (CPCTC)

Back 32

Two triangles are congruent if and only if their corresponding parts are congruent.

Hint 32

Front 33

Isosceles Triangle Theorem

Back 33

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Hint 33

Front 34

Converse of Isosceles Triangle Theorem

Back 34

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Hint 34

Front 35

HL Theorem

Back 35

In a pair of RIGHT triangles, if the hypotenuses are congruent and one pair of legs are congruent, then the two triangles are congruent.

Hint 35

Front 36

Perpendicular Bisector Theorem

Back 36

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front 37

Converse of the Perpendicular Bisector Theorem

Back 37

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Front 38

Angle Bisector Theorem

Back 38

If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

Front 39

Converse of the Angle Bisector Theorem

Back 39

If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.