Download Book of Postulates and theorems

Book of Postulates
and theorems
By: Colton Grant
Chapter 2
• Postulate 2.1- through any two points, there is
exactly one line
Chapter 2
• Theorem 2.1- Midpoint theorem- if M is the
midpoint of AB, then AM
MB
A
M
B
Chapter 3
• Postulate 3.1- Corresponding Angles
Postulate- if two parallel lines are cut by a
transversal, then each pair of corresponding
angles is congruent
Chapter 3
• Theorem 3.1- Alternate Interior Angles
Theorem- if two parallel lines are cut by a
transversal, then each pair of alternate
interior angles is congruent
Chapter 4
• Corollary 4.3- the acute angles of a right
triangle are complementary
30
45
60
45
Chapter 4
• Corollary 4.2- there can be at most one right
or one obtuse angle in a triangle
Chapter 4
• Theorem 4.1- Angle Sum Theorem- the sum of
o
the measures of the angles of a triangle is 180
60
60
60
Chapter 5
• Corollary 5.1- the perpendicular segment from
a point to a plane the shortest segment from
the point to the plane
Chapter 5
• Theorem 5.14- SSS Inequality- if two sides of a
triangle are congruent to two sides of another
triangle and the third side in one triangle is
longer than the third side in the other, then
the angle between the pair of congruent sides
in the first triangle is greater than the
corresponding angle in the second triangle
Chapter 6
• Theorem 6.1- interior angle sum theorem- if a
convex polygon has n sides and S is the sum of
the measure of it’s interior angles, then
S=180(n-2)
S=1800
Chapter 6
• Theorem 6.2- Exterior Angle Sum Theorem- if
a polygon is convex, then the sum of the
measures of the exterior angles, one at each
vertex, is 360
2
3
1
4
6
5
Chapter 6
• Theorem 6.3- opposite sides of a
parallelogram are congruent
10
5
5
10
Chapter 7
• Postulate 7.1- Angle-Angle Similarity- if two
angles of one triangle are congruent to two
angles of another triangle, then the two
triangles are similar
Chapter 7
• Theorem 7.1- Side-Side-Side Similarity- if the
measures of the of the corresponding sides of
two triangles are proportional, then the
triangles are similar
10
5
Chapter 8
• Theorem 8.4- Pythagorean Theorem- in a right
triangle, the sum of the squares of the
measures of the legs equals the square of the
measure of the hypotenuse.
C
A
2
B
2
2
Chapter 8
• Theorem 8.6- in a 45-45-90 triangle, the
length of the hypotenuse is √2 times the
length of a leg
x √2
x
x
Chapter 9
• Corollary 9.1- reflecting an image successively
in two perpendicular lines results in a 180⁰
rotation
Chapter 9
• Theorem 9.2- if a dilation with center C and a
scale factor of r transformations A to E and B
to D, then ED=lrl (AB)
Chapter 10
• Theorem 10.3- in a circle, if a diameter (or
radius) is perpendicular to a chord, then it
bisects the chord and it’s arc
Chapter 10
• Theorem 10.9- if a line is tangent to a circle,
then it is perpendicular to the radius drawn to
the point of tangency.