2.2 Reflection and Congruence

• Congruent figures and conditions for congruence
• Reflection in a mirror line
• Reflection in the axes and in the lines y = x and y = -x
• Properties of reflection
• Lines of symmetry

• identify congruent figures and state the conditions for congruence
• reflect a figure in a given mirror line
• determine the image of a point under reflection in the axes and in y = x
• state the properties of reflection
• appreciate symmetry in the environment and in design

“What stays the same when a shape is reflected, and what changes?”

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1. Congruence
   40 min · 2 practice tasks · quiz
   When two figures are genuinely identical, and how to prove it for triangles.
2. Reflection
   40 min · 2 practice tasks · quiz
   The mirror line, the coordinate rules, and what reflection preserves.
3. SSS and SAS congruence
   40 min · 1 practice tasks · quiz
   Prove two triangles congruent from three sides, or from two sides and the angle between them.
4. ASA, AAS and RHS
   40 min · 1 practice tasks · quiz
   Prove congruence from two angles and a side, or from the hypotenuse and a leg of a right-angled triangle.
5. Corresponding parts of congruent triangles
   40 min · 1 practice tasks · quiz
   Name vertices in matching order, then read off every remaining equal side and angle.
6. Constructing a reflection in a given line
   40 min · 1 practice tasks · quiz
   Build the image of a point, then of a polygon, using a perpendicular and equal distance.
7. Reflecting figures in the axes
   40 min · 1 practice tasks · quiz
   Apply (x, y) to (x, -y) and (x, y) to (-x, y) to a whole polygon, then check congruence.
8. Reflection in y = x and y = -x
   40 min · 1 practice tasks · quiz
   Swap coordinates for y = x; swap and change both signs for y = -x.
9. Reflection in x = a and y = b
   40 min · 1 practice tasks · quiz
   When the mirror is a grid line that does not pass through the origin, the image is 2a minus x, or 2b minus y.
10. Properties of reflection
    40 min · 1 practice tasks · quiz
    Reflection is an opposite isometry of order 2: lengths stay, orientation reverses, and doing it twice undoes it.
11. Lines of symmetry of plane figures
    40 min · 1 practice tasks · quiz
    A line of symmetry is a mirror that maps a shape onto itself. Count them for triangles, quadrilaterals and regular polygons.
12. Finding the mirror line and symmetry in design
    40 min · 1 practice tasks · quiz
    Recover the mirror as the perpendicular bisector of a point and its image, then read symmetry in Kenyan patterns and structures.