Isosceles Triangle Solver
Height: -
Base Angles: -
Apex Angle: -
Area: -
Perimeter: -
Understanding Isosceles Triangles
What is an Isosceles Triangle?
An isosceles triangle has two equal sides and two equal angles. Key properties include:
- Two sides of equal length
- Two base angles are equal
- Height to base bisects the base
- Height to base creates two right triangles
- Base angles are complementary to half the vertex angle
Key Formulas
Height Formula
h = √(a² - (b²/4))
where a is equal side and b is base
Area Formula
A = (b × h)/2
Base Angles
θ = arccos(b/(2a))
Special Properties
Symmetry
Has one line of symmetry through vertex
Median Properties
Median to base is also height and angle bisector
Circle Properties
Equal distances from vertices to inscribed circle
Congruence
Two equal sides imply two equal angles
Advanced Properties
Euler Line
Contains centroid, orthocenter, and circumcenter
Equal Circles
Escribed circles on equal sides are equal
Concurrent Lines
All internal angle bisectors are concurrent
Real-World Applications
Architecture
Used in roof designs and structural supports
Engineering
Applied in bridge construction and truss design
Design
Common in logo design and symmetrical patterns
Construction
Essential in building stable structures