4.1 Properties and Constructions

• Parallel lines have the same slope.


  True
• The slope of perpendicular lines is the negative reciprocal of each other.


  True
• Similar triangles have corresponding angle measures that are equal
• The radius of a circle is the distance from the center to the edge
• The circumference of a circle is calculated using the formula C = πd.


  True
• What is the approximate value of π (pi)?

  3.14
• Steps to bisect a line using a compass and straightedge:

  1️⃣ Place compass at one end of the line and draw an arc above and below it

  2️⃣ Without changing compass width, repeat from the other end

  3️⃣ Draw a straight line connecting the intersection points of the arcs
• Parallel lines have equal slopes
• What is a defining characteristic of parallel lines?

  Never intersect
• Perpendicular lines intersect at a right
• What is the angle of intersection between parallel lines?

  0 degrees
• What tools are used to construct geometric shapes accurately?

  Compass and ruler
• Congruent triangles have all corresponding side lengths and angle measures that are equal
• Similar triangles have the same shape but different sizes.


  True
• Match the triangle property with its description:

  Congruent Triangles ↔️ Exactly the same size and shape

  Similar Triangles ↔️ Same shape, different size
• What is true about the side lengths of congruent triangles?

  They are equal
• Congruent and similar triangles are used in construction and surveying.

  True
• What is the angle of intersection between perpendicular lines?

  90 degrees
• Match the quadrilateral with its properties:

  1️⃣ Parallelogram: Yes parallel sides, No perpendicular sides

  2️⃣ Rectangle: Yes parallel sides, Yes perpendicular sides, No equal sides

  3️⃣ Square: Yes parallel sides, Yes perpendicular sides, Yes equal sides

  4️⃣ Rhombus: Yes parallel sides, No perpendicular sides, Yes equal sides

  5️⃣ Kite: No parallel sides, No perpendicular sides, Pair of adjacent equal sides
• Quadrilaterals are four-sided polygons
• Match the quadrilateral with its properties:

  Parallelogram ↔️ Yes parallel sides, No perpendicular sides

  Rectangle ↔️ Yes parallel and perpendicular sides, Equal angles

  Square ↔️ Yes parallel and perpendicular sides, Equal sides and angles

  Rhombus ↔️ Yes parallel sides, Equal sides

  Kite ↔️ No parallel or perpendicular sides, Pair of adjacent equal sides
• What is the relationship between the diameter and the radius of a circle?

  d = 2r
• What is the first step in drawing a perpendicular line from a point on a given line using a compass and straightedge?

  Draw arcs on both sides equally
• Perpendicular lines intersect at right angles (90 degrees).


  True
• What is the relationship between the slopes of perpendicular lines?

  Negative reciprocals
• Match the property with the type of triangle:

  Congruent Triangles ↔️ Equal side lengths and angle measures

  Similar Triangles ↔️ Proportional side lengths and equal angle measures
• What is a quadrilateral?

  A four-sided polygon
• What is the approximate value of π used in the circumference formula?

  3.14
• Match the property of a circle with its formula:

  Diameter ↔️ d = 2r

  Circumference ↔️ C = πd

  Radius ↔️ r
• Geometric constructions using a compass and straightedge involve creating precise shapes
• Steps to bisect a line using a compass and straightedge:

  1️⃣ Place the compass at one end of the line and draw an arc above and below the line

  2️⃣ Without changing the compass width, repeat from the other end of the line

  3️⃣ Draw a straight line connecting the intersection points of the arcs
• What is one key property of an angle bisector?

  Divides the angle into two equal parts
• The diameter of a circle is twice its radius
• The circumference of a circle is calculated using the formula C = 2πr.


  True
• What is the definition of the radius of a circle?

  Distance from center to edge
• The diameter of a circle is twice its radius
• The circumference of a circle is calculated using the formula C = πd


  True
• To bisect an angle, you first draw an arc intersecting both sides of the angle


  True
• What type of triangle is formed when constructing an equilateral triangle from a line segment?

  Equilateral
• A perpendicular bisector intersects a line segment at a 90-degree angle.