Overview
This lecture covers the properties of triangles, types of triangles, angle facts, and how to solve geometric problems involving interior and exterior angles of triangles as well as parallel lines.
Properties of Triangles
- The sum of interior angles in any triangle is always 180 degrees.
- An exterior angle of a triangle equals the sum of the two opposite interior angles.
Types of Triangles
- A scalene triangle has no equal sides and all angles are different.
- An isosceles triangle has two equal sides and two equal opposite angles.
- An equilateral triangle has three equal sides and each angle measures 60 degrees.
- A right-angled triangle has one 90-degree angle; the side opposite this angle is called the hypotenuse.
Angle Facts with Parallel Lines
- Corresponding angles are equal when two lines are parallel (identified by the "F" shape).
- Alternate angles are equal when two lines are parallel (identified by the "Z" or "N" shape).
- Vertically opposite angles are equal when two lines intersect.
Sample Problems and Solutions
- Use exterior angle fact to solve for unknowns: e.g., 2x (exterior) = 50° + (x+10)°.
- In isosceles triangles, set equal angles when solving equations.
- Apply parallel line angle facts (corresponding, alternate) to find unknown angles.
- Use supplementary angles on a straight line: angles sum to 180 degrees.
Key Terms & Definitions
- Interior angles — angles inside a triangle; sum to 180°.
- Exterior angle — angle formed by extending one side of triangle; equals sum of opposite interior angles.
- Scalene triangle — no equal sides; all angles different.
- Isosceles triangle — two equal sides; two equal angles.
- Equilateral triangle — three equal sides and angles; each angle is 60°.
- Right-angled triangle — one angle is 90°.
- Hypotenuse — side opposite the right angle in a right-angled triangle.
- Corresponding angles — equal when parallel lines are cut by a transversal (F-shape).
- Alternate angles — equal when parallel lines are cut by a transversal (Z- or N-shape).
- Vertically opposite angles — equal angles formed when two lines cross.
- Supplementary angles — angles that sum to 180 degrees.
Action Items / Next Steps
- Review previous Grade 8 and 9 lessons on triangles and angle facts as needed.
- Practice solving triangle problems using these properties and angle facts.
- Prepare for the upcoming test by reviewing notes and sample problems.