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Geometry > Postulates, Proofs, and Properties > Flashcards

Postulates, Proofs, and Properties Flashcards

0
Q

What is the point and line postulate?

A

Through any two points there is exactly one line.

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1
Q

What is a postulate?

A

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

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2
Q

What is the three point plane postulate?

A

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

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3
Q

What is the segment addition postulate?

A

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

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4
Q

What is the angle addition postulate?

A

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

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5
Q

What is the definition of complimentary angles?

A

Two angles whose sum is 90 degrees

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6
Q

What is the definition of supplementary angles?

A

Two angles whose sum is 180 degrees

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7
Q

What is the definition of vertical angles?

A

Two angles that are directly across from each other

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8
Q

What is the theorem of vertical angles?

A

Vertical angles are congruent or equal in degree

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9
Q

What is the definition of an angle bisector?

A

An angle bisector splits an angle into two equal angles

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10
Q

What is the definition of a linear pair?

A

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

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11
Q

What are the Properties of Equality?

A

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

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12
Q

What does the Addition Property of Equality state?

A

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

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13
Q

What does the Subtraction Property of Equality state?

A

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

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14
Q

What does the Multiplication Property of Equality state?

A

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

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15
Q

What does the Division Property of Equality state?

A

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

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16
Q

What does the Reflexive Property of Equality state?

A

a=a

17
Q

What does the Symmetric Property of Equality state?

A

If a=b then b=a

18
Q

What does the Transitive Property of Equality state?

A

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

19
Q

What does the Substitution Property of Equality state?

A

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

20
Q

What is the definition of Perpendicular Lines?

A

Lines that form right (90°) angles

21
Q

What is true if a transversal cuts two parallel lines?

A
  • 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
22
Q

What is the definition of a Perpendicular Bisector?

A

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

23
Q

What is the Perpendicular Transversal Theorem?

A

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

24
Q

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

A

Then the two lines are parallel to each other

25
Q

What is an Acute Triangle?

A

A triangle with 3 Acute Angles

26
Q

What is a Right Triangle?

A

A triangle with 1 right angle

27
Q

What is an Obtuse Triangle?

A

A triangle with 1 obtuse angle

28
Q

What is an Equiangular Triangle

A

A triangle with 3 equal angles

29
Q

What is a Scalene Triangle?

A

A triangle with no equal sides

30
Q

What is an Isosceles Triangle?

A

A triangle with 2 equal angles

31
Q

What is an Equilateral Triangle?

A

All 3 sides are equal

32
Q

What two triangle side/angle combinations are completely impossible?

A

Equilateral right triangles

Equilateral obtuse triangles

33
Q

What does the right triangle say about the other two angles

A

The acute angles in a right triangle are complementary

34
Q

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

A

60°

35
Q

Why are exterior angles significant

A

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

36
Q

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

A

The third angle in each triangle

37
Q

What is true when an isosceles has two equal sides

A

It has two equal angles

38
Q

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

A

The angles are equal

“Equal sides, equal angles”

39
Q

What are the 5 ways to prove triangles congruent?

A 
SSS
SAS
AAS
ASA
HL (right)
40
Q

What 2 ways cannot be used to prove triangles congruent?

A

AAA

ASS

Geometry (3 decks)

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