Download Geometry MASTER Theorem Notebook List 1.4

Geometry MASTER Theorem Notebook List
1.4: Introductions
midpoint of a segment (use glossary for this one)
Midpoint Formula
Distance Formula (use the index in the back of the book to find the correct page)
2.1 Exploring Patterns
line segment right angle
ray obtuse angle
opposite rays straight angle
collinear interior of an angle
angle exterior of an angle (must use glossary)
acute angle adjacent angles
2.2 Structure of Geometry
Segment Addition Postulate
Angle Addition Postulate
2.3 Segment and Angle Relationships
congruent segments
congruent angles
midpoint
segment bisector
angle bisector
perpendicular lines
a line is perpendicular to a plane …
2.4 Conditional Statements
Point, Line and Plane Postulates: Postulates 5 through 10
2.5 Reasoning with Properties
Properties of Equality (all 8 of them, from the blue box on p. 84)
Properties of Congruence (all 3 of them, from the blue box on p. 85)
2.6 Deductive Reasoning
vertical angles
linear pair
complementary angles
supplementary angles
Linear Pair Postulate
Thm 2.1: Congruent Supplements Theorem
Thm 2.2: Congruent Complements Theorem
Thm 2.3 Vertical Angles Theorem
3.1 Lines and Planes
1) parallel lines
2) intersecting lines
3) oblique lines
4) skew lines
5) Theorem 3.1
6) Theorem 3.2
3.2 Connections to Algebra
1) Postulate 12
2) Postulate 13: Parallel Postulate
3) Postulate 14: Perpendicular Postulate
3.4 Styles of Proof
1) Theorem 3.3
2) Theorem 3.4
3) Theorem 3.5
3.5 Properties of Parallel Lines
1) transversal
2) corresponding angles
3) alternate interior angles
4) alternate exterior angles
5) consecutive interior angles
6) Postulate 15: Corresponding Angles Postulate
7) Theorem 3.6: Alternate Interior Angles Thm
8) Theorem 3.7: Consecutive Interior Angles Thm
9) Theorem 3.8: Alternate Exterior Angles Thm
10) Theorem 3.9: Perpendicular Transversal Thm
3.6 Proving Lines are Parallel
1) Postulate 16: Corresponding Angles Converse
2) Theorem 3.10: Alternate Interior Angles Converse
3) Theorem 3.11: Consecutive Interior Angles Converse
4) Theorem 3.12: Alternate Exterior Angles Converse
4.1 Congruent Triangles
1) congruent triangles
2) Classification by sides
a. Equilateral triangle
b. Isosceles triangle
c. Scalene triangle
3) Classification by angles
a. Acute triangle
b. Equiangular triangle
c. Right triangle
d. Obtuse triangle
4) vertex
5) opposite side
6) adjacent side
7) legs of a right triangle
8) hypotenuse of a right triangle
9) legs of an isosceles triangle
10) Thm 4.1: Properties of Congruent Triangles
4.2 Angles of a Triangle
1) interior angle
2) exterior angle
3) Thm 4.2: Triangle Sum Thm
4) Thm 4.3: Third Angles Thm
5) Thm 4.4
6) Thm 4.5: Exterior Angles Thm
7) Thm 4.6 Exterior Angles Inequality Thm
4.3 Proving that Triangles are Congruent
1) Postulate 17: Side-Side-Side (SSS) Congruence Postulate
2) Postulate 18: Side-Angle-Side (SAS) Congruence Postulate
4.4 More Ways to Prove that Triangles are Congruent
1) Postulate 19: Angle-Side-Angle (ASA) Congruence Postulate
2) Theorem 4.7: Angle-Angle-Side (AAS) Congruence Theorem
4.6 Isosceles and Right Triangles
1) base angles
2) Thm 4.8: Base Angles Thm
3) Thm 4.9
4) Corollary to Thm 4.8
5) Corollary to Thm 4.9
6) Thm 4.10: Hypotenuse-Leg (HL) Congruence Thm
4.5 Using Congruent Triangles
1) CPCTC
5.1 Parts of Triangles
1) Perpendicular Bisector
2) Thm 5.1: Perpendicular Bisector Thm
3) Thm 5.2: Perpendicular Bisector Converse
4) Thm 5.3: Angle Bisector Thm
5) Thm 5.4: Angle Bisector Conv.
6) distance between a point and line
5.2 Special Segments in a Triangle
1) Perpendicular Bisector of a Triangle
2) Angle Bisector of a Triangle
3) Median
4) Altitude
5) Concurrent
6) circumcenter
7) incenter
8) centroid
9) orthocenter
10) Thm 5.5: Concurrency Properties
5.3 Midsegment Theorem
1) midsegment
2) Thm 5.6: Midsegment Theorem
5.4 Inequalities in One Triangle
1) Thm 5.7
2) Thm 5.8
3) Thm 5.9: Triangle Inequality Thm
5.5 Inequalities in Two Triangles
1) Thm 5.10: Hinge Thm
2) Thm 5.11: Converse of Hinge Thm
6.1 Polygons
1) polygon
2) convex
3) concave
4) diagonal
5) equilateral
6) equiangular
7) regular
8) chart on Page 268
6.2 Angles of Polygons
1) Thm 6.1: Polygon Interior Angle Thm
2) Corollary 6.1
3) Thm 6.2: Polygon Exterior Angle Thm
4) Corollary 6.2
6.3 Properties of Parallelograms
1) parallelogram
2) Properties of Parallelograms
a. Thm 6.3
b. Thm 6.4
c. Thm 6.5
3) Thm 6.6: Diagonals of a Parallelogram
6.4 Proving Quadrilaterals are Parallelograms
1) Thm 6.7
2) Thm 6.8
3) Thm 6.9
4) Thm 6.10
5) Thm 6.11
6.5 Special Parallelograms
1) rhombus
2) rectangle
3) square
4) Thm 6.12
5) Thm 6.13
6) Thm 6.14
7) Thm 6.15
8) Thm 6.16
6.6 Trapezoids
1) Trapezoid
2) Isosceles trapezoid
3) base angles
4) Thm 6.17: Trapezoid Base Angles Thm
5) Thm 6.18: Trapezoid Diagonals Thm
6) Thm 6.19
7) Thm 6.20
8) midsegment
9) Thm 6.21: Midsegment Thm for Trapezoids
8.1 Ratios and Proportions
1) ratio
2) proportion
3) means
4) extremes
5) Properties of Proportions
8.2 Problem Solving with Proportions
1) Additional Properties of Proportions
8.3 Similar Polygons
1) similar polygons
2) scale factor
3) Thm 8.1
8.4 Similar Triangles
1) Post. 20: Angle-Angle (AA) Similarity Post.
8.5 Proving Triangles Similar
1) Thm 8.2: Side-Side-Side (SSS) Similarity Thm
2) Thm 8.3 Side-Angle-Side (SAS) Similarity Thm
8.6 Proportions in Similar Triangles
1) Thm 8.4: Triangle Proportionality Thm
2) Thm 8.5: Triangle Proportionality Converse
3) Thm 8.6
4) Thm 8.7
9.1: Right Triangles
Thm 9.1
Thm 9.2
Thm 9.3
geometric mean (again!)
9.2: Pythagorean Theorem
Thm 9.4
Pythagorean Triple
9.3: Converse of the Pythagorean Theorem
Thm 9.5: Converse of the Pythagorean Thm
Thm 9.6
Thm 9.7
9.4: Special Right Triangles
Thm 9.8
Thm 9.9
9.5: Trigonometric Ratios
trigonometric ratio
Trigonometric Ratios (entire blue box)
9.6: Solving Right Triangles
solving a right triangle … (include 3 parts)
10.1: Circles
circle
- interior
- exterior
chord
diameter
radius
tangent
point of tangency
secant
common tangent
- common external tangent
- common internal tangent
tangent circles
concentric circle (use glossary)
congruent circles
10.2: Properties of Tangents
Thm 10.1
Thm 10.2
Thm 10.3
inscribed circle
circumscribed circle
10.3 Central Angles and Arcs
central angle
minor arc
measure of a minor arc
semicircle
major arc
measure of a major arc
adjacent arcs
Postulate 21: Arc Addition Postulate
congruent arcs
Thm 10.4
10.4 Arcs and Chords
Thm 10.5
Thm 10.6
Thm 10.7
Thm 10.8
10.5: Inscribed Angles
inscribed angles
intercepted arc
Thm 10.9
Thm 10.10
Thm 10.11
Thm 10.12
10.6: Other Angle Relationships
Thm 10.13
Thm 10.14
Thm 10.15
10.7: Equation of a Circle
standard equation of a circle
11.1: Area and Perimeter
perimeter
linear measurement
area
Post. 22: Area of a Square
Post. 23: Area Congruence
Post. 24: Area Addition
Thm 11.1: Area of a Rectangle
11.2: Areas of Parallelograms and Triangles
Thm 11.2: Area of a Parallelogram
corresponding height
Thm 11.3: Area of a Triangle
11.3: Areas of other Quadrilaterals
Thm 11.4: Area of a Trapezoid
Thm 11.5
11.4: Areas of Regular Polygons
Thm 11.6: Area of an Equilateral Triangle
center of a regular polygon
radius of a regular polygon
apothem
central angle of a regular polygon
Thm 11.7: Area of a Regular Polygon
11.5/11.6: Circumference and Area of Circles
circumference
Thm 11.8: Circumference of a Circle
arc length
Arc Length Corollary
Thm 11.9: Area of a Circle
sector
Thm 11.10: Area of a Sector
segment of a circle
11.7: Area of Similar Polygons
Thm 11.11: Area of Similar Polygons
12.1: Solids
polyhedron
face
edge
vertex
surface
convex
regular polyhedron
tetrahedron
octahedron
dodecahedron
icosahedron
12.2: Surface Area of Prisms and Cylinders
prism
altitude/height
right prism
surface area
Thm 12.2 Surface Area of Right Prism
circular cylinder
right cylinder
Thm 12.3 Surface Area of Right Cylinder
12.4: Volume of Prisms and Cylinders
volume
Post 25: Volume of Cube
Thm 12.7 Volume of a Prism
Thm 12.8 Volume of a Cylinder
12.3: Surface Area of Pyramids and Cones
pyramid
regular pyramid
Thm 12.4 Surface Area of Regular Pyramid
circular cone
right cone
Thm 12.5 Surface Area of a Right Cone
12.5: Volume of Pyramids and Cones
Thm 12.9 Volume of a Pyramid
Thm 12.10 Volume of a Cone
12.6: Surface Area and Volume of Spheres
sphere
hemispheres
Thm 12.11 Surface Area of a Sphere
Thm 12.12 Volume of a Sphere
12.7: Similar Solids
similar solids
scale factor
Thm 12.13