Triangle_Theorems_Presentation_With_Notes.pptx

Triangle_Theorems_Presentation_With_Notes.pptx

• 1.
  Triangle Sum Theorem Understandingthe angles of a triangle
• 2.
  Introduction • What doyou notice about the angles in a triangle? • - Different types of triangles: • • Acute • • Right • • Obtuse
• 3.
  The Theorem • Thesum of the interior angles of a triangle is always 180°. • Formula: • ∠A + B + C = 180° ∠ ∠
• 4.
  Proof (Sketch Idea) •1. Draw a line parallel to the base through the opposite vertex. • 2. Use alternate interior angles. • 3. The three angles form a straight line (180°).
• 5.
  Examples • Example 1:If A = 40° and B = 90°, find C. ∠ ∠ ∠ • Solution: 40° + 90° + C = 180° → C = 50° ∠ ∠ • Example 2: If A = 120° and B = 30°, find ∠ ∠ C. ∠ • Solution: 120° + 30° + C = 180° → C = 30° ∠ ∠
• 6.
  Applications • - Solvinggeometry problems • - Basis for trigonometry • - Construction and navigation • - Real-world example: roof trusses, triangular road signs
• 7.
  Practice Questions • 1.If A = 70° and B = 60°, find C. ∠ ∠ ∠ • 2. If A = 100° and B = 40°, find C. ∠ ∠ ∠ • 3. Identify each triangle as acute, right, or obtuse.
• 8.
  Summary • - Thesum of angles in any triangle = 180° • - Formula: A + B + C = 180° ∠ ∠ ∠ • - Key tool in solving geometry problems
• 9.
  Thank You • Canyou think of another way to prove the theorem?
• 10.
  Exterior Angle Theorem •The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. • Formula: Exterior = Remote₁ + Remote₂ ∠ ∠ ∠
• 11.
  Example: Exterior AngleTheorem • If A = 50° and B = 60°, find exterior C. ∠ ∠ ∠ • Solution: C(exterior) = A + B = 50° + 60° ∠ ∠ ∠ = 110°
• 12.
  Isosceles Triangle Theorem •In an isosceles triangle, the angles opposite the equal sides are equal.
• 13.
  Example: Isosceles Triangle Theorem •If a triangle has two equal sides and A = 70°, ∠ find B and C. ∠ ∠ • Solution: B = C = (180° - 70°) / 2 = 55° ∠ ∠
• 14.
  Extended Summary • -Triangle Sum Theorem • - Exterior Angle Theorem • - Isosceles Triangle Theorem • - Applications & Practice
• 15.
  Practice: Triangle Theorems •1. Triangle Sum Theorem: • If A = 65° and B = 85°, find C. ∠ ∠ ∠ • 2. Exterior Angle Theorem: • If A = 40° and B = 50°, find the exterior ∠ ∠ angle at C. ∠ • 3. Isosceles Triangle Theorem: • In an isosceles triangle, if the vertex angle is