9th Grade Geometry Study Guide
Fundamental Concepts
● Points, Lines, and Planes:
○ Point: A specific location in space.
○ Line: A straight path that extends infinitely in both directions.
○ Plane: A flat surface that extends infinitely in all directions.
○
○ Collinear points: Points that lie on the same line.
○ Coplanar points: Points that lie on the same plane.
○
● Angles:
○ Acute angle: An angle less than 90 degrees.
○ Right angle: An angle exactly 90 degrees.
○ Obtuse angle: An angle greater than 90 degrees but less than 180 degrees.
○ Straight angle: An angle exactly 180 degrees.
○ Reflex angle: An angle greater than 180 degrees but less than 360 degrees.
○
○ Angle bisector: A ray that divides an angle into two congruent angles.
● Line Segments and Rays:
○ Line segment: A part of a line with two endpoints.
○ Ray: A part of a line with one endpoint.
● Parallel and Perpendicular Lines:
○ Parallel lines: Lines that never intersect.
○ Perpendicular lines: Lines that intersect at a 90-degree angle.
● Transversals: A line that intersects two or more lines.
○ Alternate interior angles: Non-adjacent interior angles on opposite sides of the
transversal.
○ Corresponding angles: Angles in corresponding positions on the same side of
the transversal.
○ Same-side interior angles: Interior angles on the same side of the transversal.
Triangles
● Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
●
● Angle-Side-Angle (ASA) Congruence Postulate: If two angles and the included side
of one triangle are congruent to two angles and the included side of another triangle,
then the triangles are congruent.
●
Fundamental Concepts
● Points, Lines, and Planes:
○ Point: A specific location in space.
○ Line: A straight path that extends infinitely in both directions.
○ Plane: A flat surface that extends infinitely in all directions.
○
○ Collinear points: Points that lie on the same line.
○ Coplanar points: Points that lie on the same plane.
○
● Angles:
○ Acute angle: An angle less than 90 degrees.
○ Right angle: An angle exactly 90 degrees.
○ Obtuse angle: An angle greater than 90 degrees but less than 180 degrees.
○ Straight angle: An angle exactly 180 degrees.
○ Reflex angle: An angle greater than 180 degrees but less than 360 degrees.
○
○ Angle bisector: A ray that divides an angle into two congruent angles.
● Line Segments and Rays:
○ Line segment: A part of a line with two endpoints.
○ Ray: A part of a line with one endpoint.
● Parallel and Perpendicular Lines:
○ Parallel lines: Lines that never intersect.
○ Perpendicular lines: Lines that intersect at a 90-degree angle.
● Transversals: A line that intersects two or more lines.
○ Alternate interior angles: Non-adjacent interior angles on opposite sides of the
transversal.
○ Corresponding angles: Angles in corresponding positions on the same side of
the transversal.
○ Same-side interior angles: Interior angles on the same side of the transversal.
Triangles
● Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
●
● Angle-Side-Angle (ASA) Congruence Postulate: If two angles and the included side
of one triangle are congruent to two angles and the included side of another triangle,
then the triangles are congruent.
●
