2.5 Geometry

• A circle has infinite line and rotational symmetry
• Understanding the properties of basic geometric shapes is important in mathematics.


  True
• What is the area formula for a triangle?

  $\frac{1}{2}bh$
• The angle between a tangent and a chord is equal to the angle in the alternate segment.

  True
• A circle has infinite line and rotational symmetry
• Opposite angles in a cyclic quadrilateral add up to 180 degrees.


  True
• In Pythagoras' theorem, 'a' and 'b' represent the lengths of the shorter sides.


  True
• Match the trigonometric ratio with its definition:

  Sine ↔️ Opposite / Hypotenuse

  Cosine ↔️ Adjacent / Hypotenuse

  Tangent ↔️ Opposite / Adjacent
• What are the main types of transformations in geometry?

  Rotation, reflection, translation
• Match the geometric shape with its properties:

  Circle ↔️ Infinite line and rotational symmetry

  Triangle ↔️ 1 line of symmetry (isosceles)

  Square ↔️ 4 lines of symmetry
• Steps to apply circle theorems

  1️⃣ Identify the relevant arcs, angles, or segments

  2️⃣ Apply the appropriate circle theorem

  3️⃣ Calculate the missing angle or length
• What is a cyclic quadrilateral?

  Opposite angles add to 180°
• Angles in the same segment are equal


  True
• What is the volume formula for a sphere?

  $\frac{4}{3}\pi r^{3}$
• Transformation geometry deals with changing the position, size, or orientation of geometric shapes
• A rectangle has two lines of symmetry and 2-fold rotational symmetry
• The perimeter formula for a circle is $2\pi$r
• The angle at the center of a circle is twice the angle at the circumference
• Match the 3D shape with its volume and surface area formulas:

  Cube ↔️ $s^{3}$ and $6s^{2}$

  Cylinder ↔️ $\pi r^{2}h$ and $2\pi r(r + h)$

  Cone ↔️ $\frac{1}{3}\pi r^{2}h$ and $\pi r(r + l)$

  Sphere ↔️ $\frac{4}{3}\pi r^{3}$ and $4\pi r^{2}$
• What is the formula for the area of a circle?

  $\pi r^{2}$
• Match each 3D shape with its volume formula:

  Cuboid ↔️ $lwh$

  Cube ↔️ $s^{3}$

  Cylinder ↔️ $\pi r^{2} h$

  Sphere ↔️ $\frac{4}{3}\pi r^{3}$
• The three main trigonometric ratios are sine, cosine, and tangent.
• In a right-angled triangle with sides 3 and 4, the hypotenuse has a length of 5
• The tangent of an angle in a right-angled triangle is calculated as the opposite side divided by the adjacent
• Reflecting a point (x, y) over the x-axis results in the new coordinates (x, -y)
• What is the formula for the area of a circle?

  $\pi r^{2}$
• The angle at the center of a circle is twice the angle at the circumference subtended by the same arc.


  True
• What are circle theorems?

  Properties within circles
• The volume formula for a cuboid is lwh
• The sine of an angle in a right-angled triangle is the ratio of the opposite side to the hypotenuse


  True
• A rotation by 90 degrees counter-clockwise around the origin transforms (1, 0) to (0, 1)


  True
• What type of symmetry does an isosceles triangle have?

  1 line of symmetry
• The area formula for a square is $s^{2}$.


  True
• What do the opposite angles of a cyclic quadrilateral add up to?

  180 degrees
• How many lines of symmetry does a square have?

  4
• The perimeter of a shape is the total distance around it.
• The surface area of a sphere is 4\pi r^{2}</latex>.


  True
• In Pythagoras' theorem, the hypotenuse is denoted by the variable c
• Steps to calculate trigonometric ratios in a right-angled triangle

  1️⃣ Identify the opposite, adjacent, and hypotenuse

  2️⃣ Calculate Sine (sin) as opposite / hypotenuse

  3️⃣ Calculate Cosine (cos) as adjacent / hypotenuse

  4️⃣ Calculate Tangent (tan) as opposite / adjacent
• A square has four lines of symmetry and 4-fold rotational symmetry.


  True