Proving Triangle Theorems
Aligned to G-CO.C.10 — Common Core State Standards for Mathematics.
What this lesson teaches
Key triangle theorems follow from congruence and parallel-line angles. The angle-sum theorem says the interior angles of any triangle add to 180°. The isosceles triangle theorem says base angles opposite equal sides are equal. The midsegment joining two side midpoints is parallel to the third side and half its length.
Worked example
Prove the triangle angle sum is 180°. Through vertex A of triangle ABC, draw a line parallel to base BC. The two angles this line makes with sides AB and AC are alternate interior angles equal to angle B and angle C. Along the straight line at A, these two angles plus angle A form a straight angle: angle B + angle A + angle C = 180°.
Practice questions
- A triangle has angles 40° and 75°. Find the third angle.
- An isosceles triangle has a vertex angle of 50°. Find each base angle.
- A triangle has sides of length 10 and 14 with a midsegment joining their midpoints. What is the length of that midsegment if it is parallel to the third side of length 12?
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.
▶ Watch this lessonEn español
Demostrar teoremas de triángulos
Los teoremas clave de triángulos se derivan de la congruencia y de los ángulos de líneas paralelas. El teorema de la suma de ángulos dice que los ángulos interiores de cualquier triángulo suman 180°. El teorema del triángulo isósceles dice que los ángulos base opuestos a lados iguales son iguales. El segmento medio que une dos puntos medios de lados es paralelo al tercer lado y mide la mitad.
Ejemplo: Demuestra que la suma de ángulos del triángulo es 180°. Por el vértice A del triángulo ABC, traza una línea paralela a la base BC. Los dos ángulos que forma esa línea con los lados AB y AC son ángulos alternos internos iguales a los ángulos B y C. Sobre la recta en A, esos dos ángulos más el ángulo A forman un ángulo llano: ángulo B + ángulo A + ángulo C = 180°.
More Congruence lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required