Triangles are the most fundamental polygons in geometry. They have unique properties and classifications.
Equilateral: 3 equal sides
Isosceles: 2 equal sides
Scalene: No equal sides
Acute: All angles < 90°
Right: One angle = 90°
Obtuse: One angle > 90°
Sum of angles = 180°
Exterior angle = sum of opposite interior angles
Longest side opposite largest angle
Congruent triangles are identical in shape and size. There are four tests to prove congruence.
Side-Side-Side
All three sides equal
Side-Angle-Side
Two sides and included angle
Angle-Side-Angle
Two angles and included side
Right-Hypotenuse-Side
Right triangles only
Similar triangles have the same shape but different sizes. Corresponding angles are equal, sides are proportional.
AAA
All angles equal
SSS
Sides proportional
SAS
Two sides proportional, included angle equal
If triangles are similar with scale factor k:
• Corresponding lengths are in ratio k : 1
• Areas are in ratio k² : 1
• Volumes are in ratio k³ : 1
Quadrilaterals are four-sided polygons with special properties.
4 right angles, opposite sides equal
4 equal sides, 4 right angles
4 equal sides, opposite angles equal
Opposite sides parallel and equal
One pair of parallel sides
Two pairs of adjacent equal sides
1. In triangle ABC, if angle A = 65° and angle B = 45°, what is angle C?
°2. What type of triangle has sides 5cm, 5cm, and 8cm?