Geometry Chapter 3-4 Study Guide
Triangle Angle-Sum Theorem (3-12)
The sum of the measures of the angles of a triangle is 180.
Interior Angle Sum: Triangle Method
Triangle Method: Count how many triangles are formed when you connect from one vertex
"Poly" "gon"
"many" "gonu=knees (angles)"
What is the sum of all convex polygons?
360
Individual Interior Angle Formula
180 (n-2) ÷ n
Classifying Polygons
3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Enagon 12 Dodecagon n n-gon
What is the sum of all central angles in a polygon?
360
Polygon
A closed figure with segments and vertices with three or more sides.
Convex Polygon
A polygon whose extension of all sides DOES NOT enter the polygon.
Concave Polygon
A polygon whose extensions of all sides DO enter the interior.
Isosceles Triangle
A triangle with two sides congruent. The congruent sides are called the legs.
Theorem 4-5 (Bisector)
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
Interior Angle Sum: Theorem
If a convex polygon has n sides, and S is the sum of the measures of its interior angles, then S = 180(n-2).
Corollary to Theorem 4-4 (Converse)
If a triangle is equiangular, then the triangle is equilateral.
Corollary to Theorem 4-3 (Isosceles Triangle Theorem)
If a triangle is equilateral, then the triangle is equiangular.
9 Most Common Properties, Definitions, & Theorems for Triangles
1. Reflexive Property 2. Definition of a Midpoint 3. Vertical Angles are Congruent 4. Definition of an angle bisector 5. Right angles are congruent 6. Definition of a perpendicular bisector 7. Alternate Interior Angles of Parallel Lines are congruent 8. If 2 angles of a triangle are congruent to two angles of another triangle, then the third angles are congruent 9. Definition of a segment bisector
Regular Polygons
All angles and sides are congruent; equilateral & equiangular.
Congruent Triangles
All three sides and all three angles of two triangles are the same (congruent).
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Exterior Angles
Created by extending the sides of the triangle. Each exterior angle forms a line with the adjacent interior angle.
Theorem 4-6 (Hypotenuse-Leg (HL) Theorem)
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Theorem 4-4 Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
Theorem 4.1 Congruent Triangles
If two angles of one triangle are congruent to the corresponding two angles of a second triangle, then the third angles are also congruent.
Theorem 4-3 Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Triangle Exterior Angle Theorem (3-13)
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
Central Angle
The point equidistant form all vertices of a polygon.
Remote Interior Angles
When an exterior angle is formed, there are two remote interior angles that are not adjacent to the exterior angle.
