Geometry Skills Part 1 2024 PDF

Geometry Skills Part 1 2023 Types of Angles Acute Right Obtuse Less than 90° Between 90° and 180° Reflex Straight Greater t...

Geometry Skills Part 1 2023 Types of Angles Acute Right Obtuse Less than 90° Between 90° and 180° Reflex Straight Greater than 180° Angle Rules Rule: Example: Complementary Angles Complementary angles add to 90° a= 90°– 60 (comp ∠’s add to 90°) a = 30° Supplementary Angles Supplementary Angles add to 180° a° + b° = 180° a = 180° – 100 (supp. ∠’s add to 180°) a = 80° Adjacent Angles on a Straight Line Adjacent angles on a straight line add to 180° Adjacent means “next to” ∠a°+∠b°+∠c =180° a = 180° – 120 – 30 ie. the angles are sitting “next to” each other (adj. ∠’s on a st. line forming a straight line add to 180°) a = 30° Vertically Opposite Angles Vertically opposite angles are equal TIP: Angles are opposite each other, forming an “X” shape ∠a° = ∠b° a= 60° (vert. opp ∠’s are =) Angles at a Point Angles around a point add to 360° a° + b° + c° = 360° a = 360° – 30 – 60 – 40 – 60 (∠’s around a pt. add to 360°) a = 170°  Triangles Types of Triangles Equilateral Isosceles Scalene All sides are the same Two sides are the same All sides are a different length. length length All interior angles are the Base angles are the same All interior angles are a same size size different size. Angle Rules - Triangles Rule: Example: Interior Angles of an Equilateral Triangle Interior angles equilateral triangle equal 60° s° = 60° (int. ∠ equalat. Δ = 60°) s° , t°, u° = 60° Interior Angles of an Isosceles Triangle Base angles of isosceles triangle are equal q° = r° q° = 75° (base ∠ isosc. Δ = ) Interior Angles of a Triangle Interior angles of a triangle add to 180° n° + o° + p° = 180° p = 180° – 55° – 85° (int. ∠’s Δ add to 180°) p = 40° Exterior Angles of a Triangle Exterior angle of a triangle is equal to sum of opposite interior angles p° = n° + o° p = 40° + 60° (ext. ∠ Δ = sum opp. = 100° int. ∠’s) Polygons Types of Polygons Polygons- a many-sided shape Angle Rules - Polygons Rule: Example: Interior Angles of a Quadrilateral Angles inside a quadrilateral add to 360° a° + b° + c° + d° = 360° x= 360 – 110 – 100 – 75 (int. ∠’s quadrilat. add to 360°) x= 75° Interior Angles Sum Interior Angles of a Polygon = (n – 2) x 180° Where n = the number of sides n= 6 b = (n – 2) x 180° (sum int. ∠’s polygon) = (6 –2) x 180° = 720° Special Polygons Sum Interior angles of a regular polygon = (n – 2) x 180° n Where n = the number of sides n=6 Regular - all sides same length a = (6 –2) x 180 (sum int. ∠’s All interior angles same 6 regular polygon) size = 720 6 = 120° NS/MCSM 2023