4.1 Properties and Constructions

• What is a point in geometry?

  A specific location in space
• A line is a straight path connecting two points and extends infinitely in both directions
• How is the space between two intersecting lines measured?

  In degrees
• A polygon is a closed shape made up of straight line segments
• Fundamental geometric concepts form the basis for more complex shapes and constructions
• What is an acute angle?

  Measures between 0° and90°
• An obtuse angle measures between 90° and 180°
• What is a right angle?

  Exactly 90°
• A straight angle measures exactly 180°
• What is a reflex angle?

  Measures between 180° and 360°
• An equilateral triangle has all sides and angles equal
• What is an isosceles triangle?

  Two sides and two angles are equal
• All sides and angles of a scalene triangle are different
• A right-angled triangle contains one angle that measures exactly 90°
• What is a regular polygon?

  All sides and angles are equal
• An irregular polygon has sides and angles that are not all equal
• What is a convex polygon?

  All interior angles are less than 180°
• A concave polygon has at least one interior angle greater than 180°
• The sum of all exterior angles of any polygon is always 360°
• What is the measure of an acute angle?

  Between 0° and 90°
• An acute angle measures between 0° and 90°
• An obtuse angle measures between 90° and 180°.
• What is the measure of a right angle?

  Exactly 90°
• A straight angle measures exactly 180°
• A reflex angle measures between 180° and 360°.
• What is a defining property of an equilateral triangle?

  All sides and angles are equal
• An isosceles triangle has two equal sides and two equal angles
• A scalene triangle has all sides and angles different.
• What is a characteristic of a right-angled triangle?

  It contains one right angle
• A regular polygon has all sides and angles equal
• A convex polygon has all interior angles less than 180°.
• What is a defining feature of a concave polygon?

  At least one interior angle > 180°
• What is the sum of all exterior angles of any polygon?

  360°
• Steps for constructing a line using a compass and straightedge

  1️⃣ Place the compass point on one endpoint

  2️⃣ Extend the compass to the other endpoint

  3️⃣ Draw the line
• To construct an angle, you draw two arcs from the vertex using a compass.
• A perpendicular bisector is formed by drawing two intersecting arcs centered on the endpoints
• What is the purpose of constructing an angle bisector?

  To divide the angle into two equal parts
• Steps for constructing an angle using a compass and straightedge

  1️⃣ Place the compass point on the vertex

  2️⃣ Extend the compass to one side and draw an arc

  3️⃣ Repeat on the other side to create the angle
• How is a circle constructed using a compass and straightedge?

  By placing the compass on the center and drawing an arc
• What is the first step in constructing a 60° angle using a compass and straightedge?

  Draw an arc