CurriculumGrade 10Mathematics

Proving Theorems about Angles

Aligned to G-CO.C.9 — Common Core State Standards for Mathematics.

What this lesson teaches

Geometric proofs use given facts, definitions, and logical steps to reach a conclusion. Angle relationships (vertical, supplementary, parallel-line angles) are common tools.

Worked example

Vertical angles are equal: when two lines cross, the opposite angles are congruent because each pairs with the same adjacent angle to make 180°.

Practice questions

  1. If two angles are supplementary and one is 110°, find the other.
  2. Why are vertical angles always equal?
  3. Two parallel lines are cut by a transversal — name a pair of equal angles.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Demostración de teoremas sobre ángulos

Las demostraciones geométricas usan datos dados, definiciones y pasos lógicos para llegar a una conclusión. Las relaciones entre ángulos (ángulos verticales, suplementarios y ángulos formados por líneas paralelas) son herramientas comunes.

Ejemplo: Los ángulos verticales son iguales: cuando dos líneas se cruzan, los ángulos opuestos son congruentes porque cada uno forma un par con el mismo ángulo adyacente para sumar 180°.

More Geometry lessons

Using Similarity and CongruenceG-SRT.B.5Right-Triangle TrigonometryG-SRT.C.8Circles and Coordinate GeometryG-GPE.A.1Volume and Geometric ModelingG-GMD.A.1

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