"A figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle."
In geometry, angles are formed by two rays that start at a common point, and they are measured in degrees. This topic covers the different types of angles, how to measure angles, and how to calculate angle relationships.
Angle measurement: Learning how to measure angles using a protractor and understanding the different units of measurement.
Types of angles: Understanding the different types of angles such as acute, obtuse, right, straight, and reflex angles.
Angle addition and subtraction: Learning how to add and subtract angles, and understanding the properties of straight angles and complementary and supplementary angles.
Angle relationships: Understanding the properties of parallel lines cut by a transversal and the angles formed, such as corresponding, alternate, interior, and exterior angles.
Angle bisectors: Understanding what an angle bisector is, how to construct one, and the properties of the angle bisectors of different types of triangles.
Congruent angles: Understanding what it means for two angles to be congruent and learning how to identify congruent angles.
Angle properties of circles: Understanding the properties of angles in circles, such as central angles, inscribed angles, and angles formed by a tangent and a chord.
Trigonometry: Learning how to use trigonometric ratios to find missing angles in right triangles and understanding the properties of sine, cosine, and tangent functions.
Angle theorems: Understanding the different angle theorems such as the angle-angle-angle (AAA) and side-angle-side (SAS) theorems, and how they can be used to prove congruence or similarity of triangles.
Angle puzzles: Solving different types of angle puzzles and problems, and using basic logic and reasoning to find solutions.
Acute angle: An angle that measures less than 90 degrees.
Right angle: An angle that measures exactly 90 degrees.
Obtuse angle: An angle that measures greater than 90 degrees but less than 180 degrees.
Straight angle: An angle that measures exactly 180 degrees.
Reflex angle: An angle that measures greater than 180 degrees but less than 360 degrees.
Complementary angles: Two angles that add up to 90 degrees.
Supplementary angles: Two angles that add up to 180 degrees.
Adjacent angles: Two angles that share a common vertex and side, but do not overlap.
Vertical angles: A pair of non-adjacent angles formed by two intersecting lines. They have the same measure and are opposite to each other.
Alternate interior angles: A pair of angles formed when a transversal intersects two parallel lines. They are on opposite sides of the transversal and are located between the parallel lines.
Alternate exterior angles: A pair of angles formed when a transversal intersects two parallel lines. They are located on opposite sides of the transversal and are located outside the parallel lines.
Corresponding angles: A pair of angles formed when a transversal intersects two parallel lines. They occupy corresponding positions, one on each of the parallel lines, on the same side of the transversal.
Congruent angles: Two angles that have the same measure are said to be congruent.
"The sides of the angle."
"The vertex of the angle."
"Plane angles."
"In the plane that contains the rays."
"Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle."
"Angles formed by the intersection of two planes."
"Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection."
"Angular measure or simply 'angle'."
"A measure defined as the ratio of a circular arc length to its radius."
"Yes, the angle of rotation may be a negative number."
"In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation."
"Angles formed by two rays are known as plane angles, while angles formed by intersecting curves may have different properties."
"No, angles formed by the intersection of two planes are known as dihedral angles."
"The magnitude of an angle refers to its measure, rather than its physical size."
"The paragraph does not explicitly mention the units in which angles are measured."
"Angles of rotation are a measure conventionally defined as the ratio of a circular arc length to its radius."
"No, an angle is formed specifically by two rays and shares a common vertex."
"The paragraph does not mention any restrictions on the orientation of the rays."
"Yes, angles formed by the intersection of two planes (dihedral angles) can exist in three-dimensional space."