Postulates, Proofs, and Properties

Question 0

What is the point and line postulate?

Answer 0

Through any two points there is exactly one line.

Question 1

What is a postulate?

Answer 1

A postulate is a statement that is accepted as true without proof.

Question 2

What is the three point plane postulate?

Answer 2

Through any three no collinear points is exactly one plane containing them

Question 3

What is the segment addition postulate?

Answer 3

If B is between A and C then AB+BC=AC

Question 4

What is the angle addition postulate?

Answer 4

When adding two angles, another angle of greater degree is formed.

Question 5

What is the definition of complimentary angles?

Answer 5

Two angles whose sum is 90 degrees

Question 6

What is the definition of supplementary angles?

Answer 6

Two angles whose sum is 180 degrees

Question 7

What is the definition of vertical angles?

Answer 7

Two angles that are directly across from each other

Question 8

What is the theorem of vertical angles?

Answer 8

Vertical angles are congruent or equal in degree

Question 9

What is the definition of an angle bisector?

Answer 9

An angle bisector splits an angle into two equal angles

Question 10

What is the definition of a linear pair?

Answer 10

Two angles who are next two each other (adjacent) and equal 180°

Question 11

What are the Properties of Equality?

Answer 11

1) Addition Property
2) Subtraction Property
3) Multiplication Property
4) Division Property
5) Reflexive Property
6) Symmetric Property
7) Transitive Property
8) Substitution Property

Question 12

What does the Addition Property of Equality state?

Answer 12

If a=b then a+c=b+c

Question 13

What does the Subtraction Property of Equality state?

Answer 13

If a=b then a-c=b-c

Question 14

What does the Multiplication Property of Equality state?

Answer 14

If a=b then a x c = b x c

Question 15

What does the Division Property of Equality state?

Answer 15

If a=b then a/c=b/c, c does not equal 0

Question 16

What does the Reflexive Property of Equality state?

Answer 16

a=a

Question 17

What does the Symmetric Property of Equality state?

Answer 17

If a=b then b=a

Question 18

What does the Transitive Property of Equality state?

Answer 18

If a=b and b=c then a=c

Question 19

What does the Substitution Property of Equality state?

Answer 19

If a=b then a+b can be substituted for each other in an equation

Question 20

What is the definition of Perpendicular Lines?

Answer 20

Lines that form right (90°) angles

Question 21

What is true if a transversal cuts two parallel lines?

Answer 21

• Corresponding Angles are equal
• Alternate Interior Angles are equal
• Alternate Exterior Angles are equal
• Same Side Interior Angles are supplementary
• Same Side Exterior Angles are supplementary

Question 22

What is the definition of a Perpendicular Bisector?

Answer 22

A line perpendicular to a segment at the segment’s midpoint

Question 23

What is the Perpendicular Transversal Theorem?

Answer 23

If a transversal is perpendicular to one of two parallel lines, then it I’d also perpendicular to the other line.

Question 24

What happens if two coplanar lines are perpendicular to the same line?

Answer 24

Then the two lines are parallel to each other

Question 25

What is an Acute Triangle?

Answer 25

A triangle with 3 Acute Angles

Question 26

What is a Right Triangle?

Answer 26

A triangle with 1 right angle

Question 27

What is an Obtuse Triangle?

Answer 27

A triangle with 1 obtuse angle

Question 28

What is an Equiangular Triangle

Answer 28

A triangle with 3 equal angles

Question 29

What is a Scalene Triangle?

Answer 29

A triangle with no equal sides

Question 30

What is an Isosceles Triangle?

Answer 30

A triangle with 2 equal angles

Question 31

What is an Equilateral Triangle?

Answer 31

All 3 sides are equal

Question 32

What two triangle side/angle combinations are completely impossible?

Answer 32

Equilateral right triangles | Equilateral obtuse triangles

Question 33

What does the right triangle say about the other two angles

Answer 33

The acute angles in a right triangle are complementary

Question 34

How many degrees must the angles be in an equiangular/equilateral triangle?

Answer 34

60°

Question 35

Why are exterior angles significant

Answer 35

The exterior angle of a triangle equals the sum of the two remote interior angles

Question 36

If 2 angles of triangle 1 equal 2 angles of triangle 2, then what must be equal as well?

Answer 36

The third angle in each triangle

Question 37

What is true when an isosceles has two equal sides

Answer 37

It has two equal angles

Question 38

What happens when angles are opposite equal sides in a triangle?

Answer 38

The angles are equal | "Equal sides, equal angles"

Question 39

What are the 5 ways to prove triangles congruent?

Answer 39

``` SSS SAS AAS ASA HL (right) ```

Question 40

What 2 ways cannot be used to prove triangles congruent?

Answer 40

AAA | ASS