Triangle Congruence and Corresponding Parts
Aligned to G-CO.B.7 — Common Core State Standards for Mathematics.
What this lesson teaches
Using rigid motions, two triangles are congruent if and only if all three pairs of corresponding sides and all three pairs of corresponding angles are congruent. One direction: a rigid motion preserves lengths and angles, so a mapping forces the parts to match. The other direction: matching parts let you build the mapping.
Worked example
Triangles ABC and DEF have AB = DE = 5, BC = EF = 7, CA = FD = 6, and angle A = angle D, angle B = angle E, angle C = angle F. All six corresponding parts match, so a sequence of rigid motions carries ABC onto DEF, making the triangles congruent (written ABC = DEF). The order of letters shows which parts correspond.
Practice questions
- Triangle ABC = triangle DEF. If AB = 8, name the side of DEF equal to it.
- In triangle ABC = triangle XYZ, angle B = 40°. What is angle Y?
- Explain why knowing all three angles are equal is NOT enough to conclude two triangles are congruent.
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
Congruencia de triángulos y partes correspondientes
Usando movimientos rígidos, dos triángulos son congruentes si y solo si los tres pares de lados correspondientes y los tres pares de ángulos correspondientes son congruentes. Una dirección: un movimiento rígido conserva longitudes y ángulos, así que un mapeo obliga a que las partes coincidan. La otra dirección: las partes que coinciden permiten construir el mapeo.
Ejemplo: Los triángulos ABC y DEF tienen AB = DE = 5, BC = EF = 7, CA = FD = 6, y ángulo A = ángulo D, ángulo B = ángulo E, ángulo C = ángulo F. Las seis partes correspondientes coinciden, así que una secuencia de movimientos rígidos lleva ABC sobre DEF, haciéndolos congruentes (se escribe ABC = DEF). El orden de las letras muestra qué partes se corresponden.
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