Postulates, Proofs, and Properties Flashcards
What is the point and line postulate?
Through any two points there is exactly one line.
What is a postulate?
A postulate is a statement that is accepted as true without proof.
What is the three point plane postulate?
Through any three no collinear points is exactly one plane containing them
What is the segment addition postulate?
If B is between A and C then AB+BC=AC
What is the angle addition postulate?
When adding two angles, another angle of greater degree is formed.
What is the definition of complimentary angles?
Two angles whose sum is 90 degrees
What is the definition of supplementary angles?
Two angles whose sum is 180 degrees
What is the definition of vertical angles?
Two angles that are directly across from each other
What is the theorem of vertical angles?
Vertical angles are congruent or equal in degree
What is the definition of an angle bisector?
An angle bisector splits an angle into two equal angles
What is the definition of a linear pair?
Two angles who are next two each other (adjacent) and equal 180°
What are the Properties of Equality?
1) Addition Property
2) Subtraction Property
3) Multiplication Property
4) Division Property
5) Reflexive Property
6) Symmetric Property
7) Transitive Property
8) Substitution Property
What does the Addition Property of Equality state?
If a=b then a+c=b+c
What does the Subtraction Property of Equality state?
If a=b then a-c=b-c
What does the Multiplication Property of Equality state?
If a=b then a x c = b x c
What does the Division Property of Equality state?
If a=b then a/c=b/c, c does not equal 0
What does the Reflexive Property of Equality state?
a=a
What does the Symmetric Property of Equality state?
If a=b then b=a
What does the Transitive Property of Equality state?
If a=b and b=c then a=c
What does the Substitution Property of Equality state?
If a=b then a+b can be substituted for each other in an equation
What is the definition of Perpendicular Lines?
Lines that form right (90°) angles
What is true if a transversal cuts two parallel lines?
- 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
What is the definition of a Perpendicular Bisector?
A line perpendicular to a segment at the segment’s midpoint
What is the Perpendicular Transversal Theorem?
If a transversal is perpendicular to one of two parallel lines, then it I’d also perpendicular to the other line.
What happens if two coplanar lines are perpendicular to the same line?
Then the two lines are parallel to each other
What is an Acute Triangle?
A triangle with 3 Acute Angles
What is a Right Triangle?
A triangle with 1 right angle
What is an Obtuse Triangle?
A triangle with 1 obtuse angle
What is an Equiangular Triangle
A triangle with 3 equal angles
What is a Scalene Triangle?
A triangle with no equal sides
What is an Isosceles Triangle?
A triangle with 2 equal angles
What is an Equilateral Triangle?
All 3 sides are equal
What two triangle side/angle combinations are completely impossible?
Equilateral right triangles
Equilateral obtuse triangles
What does the right triangle say about the other two angles
The acute angles in a right triangle are complementary
How many degrees must the angles be in an equiangular/equilateral triangle?
60°
Why are exterior angles significant
The exterior angle of a triangle equals the sum of the two remote interior angles
If 2 angles of triangle 1 equal 2 angles of triangle 2, then what must be equal as well?
The third angle in each triangle
What is true when an isosceles has two equal sides
It has two equal angles
What happens when angles are opposite equal sides in a triangle?
The angles are equal
“Equal sides, equal angles”
What are the 5 ways to prove triangles congruent?
SSS SAS AAS ASA HL (right)
What 2 ways cannot be used to prove triangles congruent?
AAA
ASS
