4.1 Properties and Constructions

• Geometry and measures are closely related because properties in geometry are often quantified through measures
• A scalene triangle has all sides of different lengths
• Pi (π) is used in calculations involving circles


  True
• What are the properties of a square?

  Equal sides and angles
• What is the formula for the diameter of a circle?

  $d =$$2r$
• Geometry is the study of the properties and relationships of shapes, such as lines, angles, and polygons.


  True
• Order the relationship between geometry and measures:

  1️⃣ Geometry focuses on shape properties

  2️⃣ Measures quantify these properties

  3️⃣ Numerical data describes the physical world
• Match the type of angle with its classification:

  Acute ↔️ Less than 90°

  Right ↔️ Exactly 90°

  Obtuse ↔️ Greater than 90°
• A right triangle has one angle that measures 90°.


  True
• Steps to bisect a line segment using a compass and straight edge:

  1️⃣ Place the compass at one end

  2️⃣ Extend the compass beyond half the length

  3️⃣ Draw an arc above and below

  4️⃣ Repeat from the other end

  5️⃣ Connect the arc intersection points
• The line connecting the arc intersection points bisects the line segment at its midpoint.

  True
• The compass width must remain constant during geometric constructions.


  True
• Steps to construct a triangle

  1️⃣ Construct the first side

  2️⃣ Construct the second side by drawing an arc

  3️⃣ Construct the third side by drawing another intersecting arc

  4️⃣ Connect the intersection points to form the third side
• Match the quadrilateral type with its properties:

  Parallelogram ↔️ Opposite sides and angles are equal

  Rectangle ↔️ Four right angles

  Rhombus ↔️ All sides are equal

  Square ↔️ All sides equal, four right angles
• Geometry and measures are closely related because properties studied in geometry are often quantified through measures.
• What are the classifications of triangles based on their sides and angles?

  Equilateral, isosceles, scalene
• A scalene triangle has all sides of different lengths.
• Opposite sides and angles are equal in a parallelogram.

  True
• The diameter of a circle is equal to 2 times its radius.
• Concentric circles share the same center but have different radii.


  True
• Measures include length, area, and volume


  True
• Acute angles are less than 90°


  True
• Triangles can be classified based on their sides and angles
• The diagonals of a rhombus bisect at right angles
• The diameter of a circle is twice its radius


  True
• The constant pi (π) governs the relationships between the properties of a circle.


  True
• Match the circle property with its formula:

  Circumference ↔️ $C =$$2πr$

  Area ↔️ $A =$$πr^{2}$
• Geometry applies mathematical principles to understand the physical world.
• The measure of an angle in degrees describes the opening between two intersecting lines.

  True
• What are the properties of an equilateral triangle?

  All sides and angles are equal
• In a rhombus, the diagonals bisect at right angles
• Steps to bisect a line segment

  1️⃣ Place the compass at one end of the line segment

  2️⃣ Extend the compass beyond half the length of the line segment

  3️⃣ Draw an arc above and below the line segment

  4️⃣ Repeat steps 1-3 from the other end

  5️⃣ Draw a line connecting the two intersection points
• A perpendicular line intersects at a 90° angle.
• How many pieces of information are needed to construct a triangle?

  Three
• To construct an equilateral triangle, all three sides must be of equal length.
• What do measures quantify in geometry?

  Geometric properties
• Match the geometric property with its description:

  Straight lines ↔️ Measured for length and separation

  Angles ↔️ Measured in degrees

  Polygons ↔️ Defined by number of sides and angles
• What applies to the side lengths of a right triangle?

  Pythagorean theorem
• Match the quadrilateral with its unique property:

  Rhombus ↔️ Diagonals bisect at right angles

  Square ↔️ All sides equal and all angles 90°
• What is the formula for the circumference of a circle?

  $C =$$2πr$