Building distance estimates rung by rung
The cosmic distance ladder is a series of techniques, each calibrated by the previous, extending distance measurements from Earth to the edge of the observable universe. Parallax (geometric triangulation using Earth's orbit) reaches about 30,000 light-years directly. Cepheid variables, stars that pulse with a period linked to their brightness, were calibrated using nearby parallax-measured Cepheids; their brightness-period relationship (the period-luminosity relation) lets astronomers measure distant Cepheids in other galaxies. Type Ia supernovae (thermonuclear explosions of white dwarfs) are the brightest objects visible across the universe; calibrated using Cepheid distances to nearby galaxies, they extend measurements to billions of light-years.
Redshift, the cosmic expansion indicator, is the final rung. Calibrated using supernova distances, redshift maps distances to the most remote observable structures.
Why each rung must be trustworthy
An error in a lower rung propagates to all higher rungs. If parallax measurements were wrong, Cepheid calibration would be wrong, supernova distances would be wrong, and the age of the universe would be wrong. The Hipparcos satellite's parallax measurements revealed that nearby galaxies were 10 percent farther than previously thought, immediately implying the universe is older than earlier estimates suggested.
Modern measurements use multiple independent techniques at each rung, seeking agreement. Supernovae are supplemented by other distance markers (gravitational lensing, water masers, etc.). The convergence of diverse methods on consistent distances builds confidence in the cosmic framework.