Similarity Transformations
Aligned to G-SRT.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Two figures are similar when a sequence of rigid motions and a dilation maps one onto the other. For triangles this means corresponding angles are equal and corresponding sides are proportional. The common ratio of the sides is the scale factor.
Worked example
Triangle ABC has sides 3, 4, 5. Triangle DEF has sides 6, 8, 10 with equal corresponding angles. Check proportionality: 6/3 = 2, 8/4 = 2, 10/5 = 2. All ratios equal 2, so a dilation of factor 2 (with rigid motions) maps ABC onto DEF. The triangles are similar with scale factor 2.
Practice questions
- Triangle 1 has sides 5, 7, 9. Triangle 2 is similar with scale factor 3. List its side lengths.
- Two similar triangles have corresponding sides 12 and 4. What is the scale factor from the small to the large?
- If two triangles are similar, what must be true about each pair of corresponding 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.
▶ Watch this lessonEn español
Transformaciones de semejanza
Dos figuras son semejantes cuando una secuencia de movimientos rígidos y una dilatación mapea una sobre la otra. Para triángulos esto significa que los ángulos correspondientes son iguales y los lados correspondientes son proporcionales. La razón común de los lados es el factor de escala.
Ejemplo: El triángulo ABC tiene lados 3, 4, 5. El triángulo DEF tiene lados 6, 8, 10 con ángulos correspondientes iguales. Verifica la proporcionalidad: 6/3 = 2, 8/4 = 2, 10/5 = 2. Todas las razones son 2, así que una dilatación de factor 2 (con movimientos rígidos) mapea ABC sobre DEF. Los triángulos son semejantes con factor de escala 2.
More Similarity, Right Triangles & Trigonometry 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