3rd Monthly Test Flashcards
method of organizing a logical argument in a geometric proof or mathematical proof.
Two - Column Proof
contains a list of statements
Left column
provides the corresponding reasons or justifications for each statement.
Right column
statement of the facts given to be true
Given
a statement of the conclusion
Prove
an illustration that shows the given information
Diagram
provided reasons or justifications
Reasons
numbered sequentially statements that are written on the left column which must be true to prove the conclusion
Statements
a = a
Reflexive Property
If a = b, then b = a
Symmetric Property
If a = b and b = c, then a = c.
Transitive Property
If a = b, then a and b can replace each other
Substitution Property
If a = b, then a + c = b + c.
Addition Property of Equality
If a = b, then a - c = b - c.
Subtraction Property of Equality
If a = b, then a * c = b * c
Multiplication Property of Equality
Addition: a + b = b + a
Multiplication: a * b = b * a
Commutative Property
If a * (b + c) = a * b + a * c.
Distributive Property
If a = b and c ≠ 0, then a / c = b / c.
Division Property of Equality
Addition: (a + b) + c = a + (b + c).
Multiplication: (a * b) * c = a * (b * c)
Associative Property
a(b + c) = ab + ac
Distributive Property
basic geometric shape that consists of three sides and three angles
Triangle
No equal Sides
Scalene
Two sides and angles are equal
Isosceles
All sides and angles are equal
Equilateral
Triangles that are classified according to their sides are called?
Scalene, Isosceles, Equilateral Triangles
Triangles are also classified according to their angles, They are called?
Right, Obtuse, Acute, Equiangular Triangles.
A type of triangle that has one of its angles equal to 90 degrees
Right
triangle with one obtuse angle(more than 90º, less than 180º) and two acute angles.
Obtuse
All sides and angles are equal.
Equiangular
triangle that has three acute (more than 0º, less than 90º) angles.
Acute
It is a theorem in geometry that states if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.
True
It states that if THREE sides of one triangle are congruent to one corresponding side of another triangle, then the two triangles are congruent.
SSS Postulate
It states that if TWO ANGLES and a NON-INCLUDED side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.
AAS Theorems
It states that if TWO ANGLES and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
ASA Postulate
It states that if TWO SIDES and the included angle of ONE triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.
SAS Postulate
is a line, segment, or ray that cuts another line segment in two equal parts at a right angle.
Perpendicular Bisector
