Corresponding Angles

Corresponding angles are pairs of angles that are formed at the same relative positions when a transversal intersects two parallel lines. In simpler terms, when a straight line (the transversal) intersects two other lines, corresponding angles are those that occupy matching positions at each intersection point.

In the context of parallel lines and transversals, corresponding angles are always congruent, meaning they have equal measures. This geometric concept is crucial for understanding and solving problems related to the relationships between angles formed by parallel lines. The principle of corresponding angles provides a foundation for proving theorems and making geometric deductions in various mathematical applications.

Corresponding Angles Definition

• Line $\mathrm{MN}$ intersects the lines $\mathrm{PQ}$ and $\mathrm{RS}$.
• Angles $\angle a$, $\angle b$, $\angle c$ and $\angle d$ are formed at the intersection point of lines $\mathrm{PQ}$ and $\mathrm{MN}$.
• Angles $\angle w$, $\angle x$, $\angle y$ and $\angle z$ are formed at the intersection point of lines $\mathrm{RS}$ and $\mathrm{MN}$.
• The pairs of corresponding angles in the above figure are:
  • $\angle a$ and $\angle w$
  • $\angle b$ and $\angle x$
  • $\angle d$ and $\angle z$
  • $\angle c$ and $\angle y$

Corresponding Angles Theorem

• Lines $L_1$ and $L_2$ are parallel.
• Line $t$ intersects lines $L_1$ and $L_2$. Hence $t$ is the transversal.
• The pairs of corresponding angles formed by the parallel lines and transversal in the above figure are:
  • $\angle a$ and $\angle w$
  • $\angle b$ and $\angle x$
  • $\angle d$ and $\angle z$
  • $\angle c$ and $\angle y$
• Since, corresponding angles formed by two parallel lines are always equal,
  • $\angle a=\angle w$
  • $\angle b=\angle x$
  • $\angle d=\angle z$
  • $\angle c=\angle y$

Solved Examples on Corresponding Angles