4.1 Properties and Constructions

• Geometry develops spatial reasoning skills.


  True
• A quadrilateral is a closed shape with 4 sides.
• What is the measure of a straight angle?

  180°
• The sum of the interior angles of a triangle is 180°.


  True
• Geometric constructions use a compass and ruler to draw figures without precise measurements.

  True
• Quadrilaterals are polygons with 4 sides and 4 angles.

  True
• The diagonals of a parallelogram bisect each other.

  True
• Steps to construct a perpendicular bisector

  1️⃣ Draw a line segment

  2️⃣ Mark equal distances from the midpoint on both ends

  3️⃣ Connect the marked points to create the bisector
• Geometry develops spatial reasoning skills.

  True
• Match the angle type with its measure:

  Acute Angle ↔️ Less than 90°

  Right Angle ↔️ Exactly 90°

  Obtuse Angle ↔️ Greater than 90° but less than 180°

  Straight Angle ↔️ Exactly 180°
• A reflex angle is greater than 180° but less than 360°
• Triangles are polygons with 3 sides and 3 angles
• Quadrilaterals are polygons with 4 sides and 4 angles
• What do the diagonals of a parallelogram always do to each other?

  Bisect each other
• What is the first step in constructing an angle bisector?

  Draw an angle
• Steps to construct a perpendicular bisector of a line segment:

  1️⃣ Draw the line segment

  2️⃣ Use the compass to mark equal distances from the midpoint on both ends of the line segment

  3️⃣ Connect the two marked points
• To draw an equilateral triangle, mark off the same distance from each end of the base using a compass
• Congruent triangles have the same size and shape
• In similar shapes, corresponding sides are proportional
• The Angle-Side-Angle (ASA) congruence criterion requires two angles and the included side of the triangles to be equal

  True
• What is the purpose of understanding similar shapes in geometry?

  To solve problems involving scale
• Match the geometric shape with its property:

  Line ↔️ Has length, can be straight or curved

  Triangle ↔️ Closed shape with 3 sides

  Circle ↔️ Closed curved shape with no sides
• A right angle measures exactly 90 degrees
• Match the type of triangle with its classification:

  Equilateral ↔️ All sides are equal

  Isosceles ↔️ Two sides are equal

  Scalene ↔️ No sides are equal
• What two tools are used in geometric constructions?

  Compass and ruler
• To construct a perpendicular bisector, use the compass to mark equal distances from the midpoint
• To construct a perpendicular bisector, use the compass to mark equal distances from the midpoint
• To create an equilateral triangle, mark off the same distance from each end of the side to create the other two sides
• Two triangles are congruent if all three sides of the two triangles are equal in length, according to the SSS congruence criterion.
• Similar shapes have the same shape but different sizes
• A regular shape must have all sides and angles equal to tessellate.


  True
• What is geometry the branch of mathematics concerned with?

  Shapes, properties, relationships
• How is an angle measured?

  Degrees
• An acute angle measures less than 90°.
• How does geometry enhance spatial reasoning?

  Visualizing shapes, arrangements
• What is a key property of the diagonals of a parallelogram?

  They bisect each other
• Triangles can be classified by their side lengths (e.g., equilateral, isosceles, scalene) or angles
• Quadrilaterals can be classified by their side lengths and angles
• Key geometric constructions include bisecting a line, constructing a perpendicular, and bisecting an angle
• In geometric constructions, you can construct parallel lines by marking points at equal distances