Math is Beauty

MPP.7 · Unit 10 · Lesson 2

Name   Period

Objectives / Objetivos

Content Objective: I can use bilateral symmetry to describe structure in nature and in human creations.

Language Objective: I can describe a symmetric design using the words mirror image, line of symmetry, and balance.

Key Idea / Idea clave

Symmetry, Geometry & Design. 1. Line of Symmetry: Divides a figure into two congruent mirror-image halves. 2. Rotational Symmetry: Shape rotates onto itself in less than a full 360° turn. 3. Geometric transformations preserve angle measures and side lengths

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
symmetric
simétrico		Having two halves that match — one side is a mirror image of the other.
Que tiene dos mitades que coinciden: un lado es la imagen reflejada del otro.
mirror image
imagen reflejada		A copy of a figure flipped across a line, so the two halves face each other.
Una copia de una figura volteada al otro lado de una línea, de modo que las dos mitades se miran entre sí.
bilateral symmetry
simetría bilateral		Reflective symmetry in plants and animals — the two sides of the body mirror each other.
La simetría reflectiva en plantas y animales: los dos lados del cuerpo se reflejan entre sí.
line of symmetry
eje de simetría		The line you can draw through a figure so each side is a reflection of the other.
La línea que puedes trazar por una figura de modo que cada lado sea el reflejo del otro.
balance
equilibrio		An even, steady arrangement — neither side feels heavier than the other.
Una disposición pareja y estable: ningún lado se siente más pesado que el otro.

Practice Preview / Vista previa de práctica

  1. What does it mean that a butterfly is symmetric?
    1. The two sides of the butterfly look like mirror images
    2. The butterfly has exactly two wings
    3. The butterfly's wings are very colorful
    4. The butterfly is larger than most insects
  2. Why do people find symmetry pleasing?
    1. Our brains are wired to favor balance, and bilateral symmetry provides balance
    2. Symmetric things are always brightly colored
    3. Symmetry only appears in rare and expensive objects
    4. Symmetric shapes are always larger than non-symmetric ones
  3. There are over 17,000 species of butterflies, and ALL butterflies have reflective symmetry. About how many of those species have reflective symmetry?
    1. All 17,000+ of them
    2. About half of them
    3. Only the most colorful ones
    4. None — symmetry is only in plants
  4. Your friend insists that only ONE of two flowers has bilateral symmetry, but both pass the mirror-image test — just across lines pointing in different directions. What is the best response?
    1. Both flowers have bilateral symmetry — a line of symmetry does not have to point the same direction in every figure
    2. Your friend is right, because a real line of symmetry must always be vertical
    3. Neither flower has bilateral symmetry, because flowers are not animals
    4. Agree with your friend, because two people should not disagree about math

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: