4.1 Properties and Constructions

• The sum of angles in a triangle is 180
• A perpendicular bisector constructs a line that is perpendicular to another line and passes through its midpoint
• What is the purpose of constructing parallel lines?

  Create lines that never intersect
• A circle has infinite rotational symmetry.


  True
• A perpendicular bisector cuts a line segment in half at a 90-degree angle.


  True
• What tool is used to construct geometric shapes precisely?

  Ruler and compass
• Steps to construct parallel lines

  1️⃣ Draw the original line

  2️⃣ Mark off a distance along the line

  3️⃣ Draw arcs from the marked points that cross the line

  4️⃣ Connect the arc intersections to create a parallel line
• Steps to construct parallel lines using a ruler and compass

  1️⃣ Draw the original line you want to construct a parallel to

  2️⃣ Mark off a distance along the original line

  3️⃣ Draw an arc that crosses the original line

  4️⃣ Repeat the arc on the other side

  5️⃣ Connect the intersection points
• Match the geometric shape with its key features:

  Triangle ↔️ Sum of angles is 180°

  Quadrilateral ↔️ Sum of angles is 360°

  Circle ↔️ Infinite symmetry
• When constructing a perpendicular bisector, the compass should be set to more than half the length of the line.


  True
• A perpendicular bisector ensures a line is divided precisely in half at a right angle.


  True
• The final line drawn in an angle bisector construction is called the angle bisector.

  True
• The angle bisector ensures the angle is precisely divided into two equal parts
• Constructing triangles involves using a ruler and compass
• A scalene triangle has three sides of equal length

  False
• The intersection points of arcs in parallel line construction must be connected to create the parallel line


  True
• The sum of angles in a quadrilateral is 360°.


  True
• Steps to construct a perpendicular bisector

  1️⃣ Draw the line segment you want to bisect

  2️⃣ From each endpoint, draw arcs above and below the line

  3️⃣ Ensure the arcs intersect

  4️⃣ Connect the intersection points with a straight line
• The sum of angles in a triangle is always 180
• An angle bisector divides an angle into two equal parts
• An angle bisector is a line that divides an angle into two equal parts
• An angle bisector ensures an angle is precisely divided into two equal parts
• Connecting the arc intersection points constructs a parallel line.
• Match the step with its description in constructing parallel lines:

  Step 1 ↔️ Draw the original line

  Step 2 ↔️ Mark off a distance along the line

  Step 3 ↔️ Draw an arc that crosses the line

  Step 4 ↔️ Repeat the arc on the other side

  Step 5 ↔️ Connect the intersection points
• A perpendicular bisector cuts a line in half at a 90-degree angle.
• An angle bisector divides an angle into two equal parts.
• An angle bisector divides an angle into two equal parts.
• What is an angle bisector?

  A line dividing an angle
• To construct parallel lines, you must first draw the original line


  True
• Steps to construct an equilateral triangle using a ruler and compass

  1️⃣ Draw a line segment AB

  2️⃣ Using the compass, mark off the length of AB on both sides to create points C and D

  3️⃣ Connect points A, B, and C (or B, C, and D) to form the equilateral triangle
• What is the first step in constructing a perpendicular bisector?

  Draw the line segment
• What type of symmetry does a circle have?

  Infinite rotational and mirror
• An angle bisector divides an angle into two equal parts.


  True
• What is the sum of angles in a quadrilateral?

  360°
• Steps to construct a perpendicular bisector

  1️⃣ Draw the line segment you want to bisect

  2️⃣ From each endpoint, draw arcs above and below the line

  3️⃣ Ensure the arcs intersect

  4️⃣ Connect the intersection points with a straight line
• What is the key feature of parallel lines?

  They never intersect
• Steps to construct an angle bisector

  1️⃣ Draw the angle you want to bisect

  2️⃣ From the vertex, draw arcs that cross the sides of the angle

  3️⃣ Connect the points where the arcs intersect the sides

  4️⃣ The resulting line is the angle bisector
• What is the first step in constructing parallel lines?

  Draw the original line
• When drawing a line parallel to AB, 3 cm away, you first mark off 3 cm along AB.


  True
• The sum of angles in a triangle is 180°.