Angles in Triangles

Angles in Triangles

Angle Properties

• The sum of interior angles in a triangle is always 180°.
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Types of Angles

• Acute Angle: An angle whose measure is between 0° and 90°.
• Right Angle: An angle whose measure is 90°.
• Obtuse Angle: An angle whose measure is between 90° and 180°.
• Straight Angle: An angle whose measure is 180°.

Angle Relationships

• Complementary Angles: Two angles whose sum is 90°.
• Supplementary Angles: Two angles whose sum is 180°.
• Vertical Angles: Two angles formed by two intersecting lines, always equal in measure.

Angle Theorems

• Angle Sum Theorem: The sum of interior angles in a triangle is always 180°.
• Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
• Corresponding Angles Theorem: If two triangles are similar, corresponding angles are equal.

Angle Properties

• The sum of interior angles in a triangle is always 180°, a fundamental property of triangles.
• The measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles, a key relationship between interior and exterior angles.

Types of Angles

• Acute Angle: Defined as an angle with a measure between 0° and 90°, indicating a sharp or narrow angle.
• Right Angle: A 90° angle, a fundamental angle in geometry and trigonometry.
• Obtuse Angle: An angle with a measure between 90° and 180°, a wider angle than an acute angle.
• Straight Angle: A 180° angle, essentially a straight line.

Angle Relationships

• Complementary Angles: Two angles with a sum of 90°, a key concept in trigonometry and geometry.
• Supplementary Angles: Two angles with a sum of 180°, another important relationship between angles.
• Vertical Angles: Two angles formed by two intersecting lines, always equal in measure, a fundamental concept in geometry.

Angle Theorems

• Angle Sum Theorem: The sum of interior angles in a triangle is always 180°, a foundational theorem in geometry.
• Exterior Angle Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles, a key theorem in triangle geometry.
• Corresponding Angles Theorem: If two triangles are similar, corresponding angles are equal, a crucial theorem in similar triangles.