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

60

45

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 the measures of the angles of a triangle is 180

o

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

1

2

3

4

56

Chapter 6

• Theorem 6.3- opposite sides of a parallelogram are congruent

10

55

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

5

10

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.

A2

B2

C2

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

x

x √2

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.