Geometry H Ch.2 Review
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42 Terms
Polygon Definition
A closed plane figure whose sides are line segments that intersect only at the endpoints.
Convex vs. Concave Polygon
Convex has no vertex inside; concave has at least one vertex inside.
Polygon Diagonal
A segment joining two nonconsecutive vertices.
Diagonal Theorem
Total number of diagonals D = n(n - 3) / 2, where n is the number of sides.
Polygon Interior Angle Sum Theorem
The sum S of interior angles is S = (n - 2) * 180°.
Regular Polygon Interior Angle Corollary
The measure of each interior angle is I = (n - 2) * 180° / n.
Polygon Exterior Angle Sum Corollary
The sum of the measures of the exterior angles of a polygon is 360°.
Regular Polygon Exterior Angle Formula
The measure of each exterior angle of a regular polygon is E = 360° / n.
Triangle Definition
Three segments joining three non-collinear points.
Triangle Classification by Sides
Scalene (no equal sides), Isosceles (at least 2 equal sides), Equilateral (all sides equal).
Triangle Classification by Angles
Acute (3 acute), Obtuse (1 obtuse), Right (1 right), Equiangular (all equal).
Triangle Angle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180°.
Triangle Exterior Angle Corollary
The measure of an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Right Triangle Complementary Corollary
The acute angles of a right triangle are complementary.
Equilateral Triangle Corollary
Each interior angle of an equilateral triangle measures 60°.
Indirect Proof Definition
A proof in which you prove that a statement is true by first assuming that its opposite is true.
Indirect Proof Steps
- Identify statement. 2. Assume opposite is true. 3. Obtain logical statements. 4. Find a contradiction.
Converse Corresponding Angles Theorem
If two lines are cut by a transversal so corresponding angles are equal, then the lines are parallel.
Converse Alternate Interior Angles Theorem
If two lines are cut by a transversal so alternate interior angles are equal, then the lines are parallel.
Three Parallel Line Theorem
If two lines are parallel to the same line, then they are parallel to each other.
Plane, Perpendicular, Parallel Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Parallel Lines
Lines in the same plane that do not intersect.
Parallel Planes
Planes that do not intersect.
Parallel Postulate
Through a point not on a line, exactly one line is parallel to the given line.
Transversal
A line that intersects two or more coplanar lines at different points.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
Point-Line Theorem
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Triangle clasification methods
Sides/Angles
Triangle angle types
Equiangular, acute, obtuse, right