## Angles and Triangles

Triangles are polygons with three sides. ### Angle Properties of Triangles

 The interior angles of a triangle always add up to 180°. ( ∠ sum of Δ) a + b + c = 180° An exterior angle of a triangle is equal to the sum of the two opposite interior angles. (ext. ∠ of Δ = sum of int.opp ∠s) w = x + y The exterior angles of a triangle always add up to 360°. (sum of ext. ∠s of Δ) m + n + p = 360° The smallest angle of a triangle is opposite the smallest side.
The largest angle of a triangle is opposite the largest side.

### Types of Triangles

 An acute − angled triangle contains no angles greater than 90° ∠A , ∠B and ∠C are all acute angles. A right − angled triangle contains an angle of 90°. ∠A = 90° An obtuse − angled triangle contains an angle between 90°and 180°. ∠A is an obtuse angle An isosceles triangle has one axis of symmetry. An isosceles triangle has two equal sides and two equal angles. sides: a = b angles: ∠A =∠B An equilateral triangle is one in which all three sides are of equal length and each interior angle is 60°. An equilateral triangle has three axes of symmetry. sides: a = b = c angles:∠A = 60°∠B = 60°∠C = 60° • Congruent triangles have the same size and shape.
• Similar triangles have the same shape. The angles of similar triangles are the same, the lengths of the corresponding sides are different
• If all of the angles and sides are different it is a scalene triangle.