Postulates: All the units

Question 1

Postulate 1: Unit 1

Answer 1

Through any 2 points there is exactly 1 line.

Question 2

Postulate 2: Unit 1

Answer 2

If 2 lines intersect, then they intersect in exactly 1 point (systems of equations.)

Question 3

Postulate 3: Unit 1

Answer 3

If 2 planes intersect , they intersect in exactly 1 line.

Question 4

Postulate 4: Unit 1

Answer 4

For any 3 noncollinear points there is exactly 1 plane containing them.

Question 5

Ruler Postulate (Postulate 5): Unit 1

Answer 5

The points on a line can be matched one-to-one with real-number coordinates so that:
a. for any 2 points there corresponds a unique positive number called the distance between two points.
b. the distance between any two points is the absolute value of the difference of their coordinates. AB = I a-b I

Question 6

Segment Addition Postulate (Postulate 6): Unit 1

Answer 6

If 3 points A, B, C are collinear and B is between A
and C, then AB + BC= AC.

Question 7

Protractor Postulate (Postulate 7): Unit 1

Answer 7

Let Ray OA, and Ray OB be opposite rays in a plane. All the rays from point O on 1 side of Ray OA can be matched one-to-one with real numbers from 0 to 180 so that
a. Ray OA is matched with 0
b. Ray OB is matched with 180
c. is Ray OC matched with x and Ray OD is matched with y, then m<COD = I x-y I

Question 8

Angle Addition Postulate (Postulate 8) : Unit 1

Answer 8

If B is in the interior of <AOC, then
m <AOB + m<BOC = m<AOC

Question 9

Postulate 9: Unit 1

Answer 9

If 2 figures are congruent, then their areas are equal.

Question 10

Postulate 10: Unit 1

Answer 10

The area of a region is the sum of the areas of its nonoverlapping parts.

Question 11

Angle Bisector Theorem (Theorem 11): Unit 2

Answer 11

If ray BD is the bisector of < ABC then
< ABD = 1/2 < ABC

Question 12

Vertical Angle Theorem; VAT
(Theorem 12): Unit 2

Answer 12

Vertical angle are congruent.

Question 13

Linear Pair Postulate (Postulate 13): Unit 2

Answer 13

2 angles that form a linear pair are supplementary.

Question 14

Linear Pair Theorem (Theorem 14): Unit 2

Answer 14

The sum of the measures of a linear pair is 180 degrees.

Question 15

Congruent Complement Theorem (Theorem 15): Unit 2

Answer 15

If 2 angles that are complementary to the same angle or to congruent angles, then they are congruent.

Question 16

Congruent Supplements Theorem (Theorem 16): Unit: 2

Answer 16

If 2 angles that are supplementary to the same angle or to congruent angles, then they are congruent.

Question 17

Common Segment Theorem (Theorem 17): Unit: 2

Answer 17

If segment AB is congruent to segment CD, then segment AC is congruent to segment BD.

Question 18

Converse of the Common Segment Theorem (Theorem 18): Unit 2

Answer 18

If AC is congruent to segment BD, then segment AB is congruent to segment CD.

Question 19

Common Angle Theorem (Theorem 19): Unit 2

Answer 19

If angle ABC is congruent to angle DBE, then angle ABD is congruent to angle CBE.

Question 20

Converse of the Common Angle Theorem (Theorem 20): Unit 2

Answer 20

If angle ABD is congruent to angle CBE, then angle ABC is congruent to angle DBE

Question 21

Corresponding Angles Postulate: (Postulate 21): Unit 3

Answer 21

If a transversal intersects two parallel lines, then the corresponding angles are congruent.

Question 22

Alternate Interior Angles Theorem (Theorem 22): Unit 3

Answer 22

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Question 23

Alternate Exterior Angles Theorem (Theorem 23): Unit 3

Answer 23

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

Question 24

Same-side Interior Angles Theorem (Theorem 24): Unit 3

Answer 24

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Question 25

Same-side Exterior Angles Theorem (Theorem 25): Unit 3

Answer 25

If a transversal intersects two parallel lines, then same-side exterior angles are supplementary.

Question 26

Converse of the Corresponding Angles Postulate: (Postulate 26): Unit 3

Answer 26

If the corresponding angles are congruent, then a transversal intersects two parallel lines.

Question 27

Converse of the Alternate Interior Angles Theorem (Theorem 22): Unit 3

Answer 27

If alternate interior angles are congruent ,then a transversal intersects two parallel lines

Question 28

Converse of the Alternate Exterior Angles Theorem (Theorem 28): Unit 3

Answer 28

If alternate exterior angles are congruent, then a transversal intersects two parallel lines

Question 29

Converse of the Same-Side Interior Angles Theorem (Theorem 29): Unit 3

Answer 29

If same-side interior angles are supplementary, then a transversal intersects two parallel lines.

Question 30

Converse of the Same-Side Exterior Angles Theorem (Theorem 30): Unit 3

Answer 30

If same-side exterior angles are supplementary, then a transversal intersects two parallel lines

Question 31

Theorem 31: Unit 3

Answer 31

All right angles are congruent.

Question 32

Theorem 34: Unit 3

Answer 32

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

Question 32

Theorem 32: Unit 3

Answer 32

If two lines are parallel to the same line, then they are parallel to each other.

Question 33

Theorem 33: Unit 3

Answer 33

If two lines are perpendicular to the same line, then they are parallel to each other.

Question 34

Theorem 35: Unit 3

Answer 34

Given line, l, and a point P not on l, there exists one and only one line through P, parallel to l.

Question 35

Triangle Sum Theorem (Theorem 36): Unit 3

Answer 35

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

Question 36

Angle Sum Theorem (Theorem 37): Unit 3

Answer 36

The measure of an exterior angle of a triangle equals the sum of it’s two remote interior angles.