Basic geometry and polygons

Honelako gehiago

Students need to know how to use a compass and a straightedge to contrust geometric figures

by Laura McGuire

Geometric Figures

by Christopher Atwood

3D GEOMETRY

by Leire Vallejo

Math Summative

by Maham Saif - T L Kennedy SS (2352)

Basic geometry and polygons

Basic Geometry: Angles

Vertically opposite angles occurs when straight lines intersect

A=B (vert. opp. ∠s)

Adjacent angles on a straight line, Represented as (Adj. ∠s on a str. line)

180°= x + 3x + 2x (adj. ∠s on a str. line)

Corresponding angles

Interior angles represented as (int. ∠s, AB//CD)

This means that corresponding angles are equal ∠a=∠d Example (Corr . ∠s, PQ//RS) Alternate angles equal ∠d=∠h Example (Alt. ∠s PQ//RS) Interior angles supplementary ∠b+∠a=180°

This also consists of two pairs of parallel lines . a line QP will have to be drawn horizontally in between angle x in order to get two Z angles , where reflex of angle x = w+z ( Alt.∠s , AA//QP) ( Alt ∠s CC//QP)

Example of corresponding angle question where a=55° as alt. ∠s is applicable

Z angle can be applied to find the other of corresponding angle

Acute angle 0°

Perpendicular lines expressed as AB⊥PQ

Special Quadrilaterals

Rectangle

two diagonal equal in length, all sides 90°

rectangles consists of 4 isosceles triangles

Usable terms:Int. ∠ of rect.)

Trapezium

At least one pair of parallel sides, Angles in between parallel sides add up to 180°

rhombus

Two pairs of parallel lines , all 4 sides equal length

Consists of 2 equal isosceles triangles , angles between each two parallel lines are the same

kite

At least 2 pairs of adjacent sides

consists of two isosceles triangles , one smaller than the other

∠DEA=∠DEC(longer diagonal BD bisects ∠ADC) =25° ∠DEC°=90° ( diagonals of kite cut each other at right angles) ∠BAD=∠BCD(opp. ∠s of kite)

parallelogram

Two pairs of parallel lines , diagonals bisect each other , angles in between add up to 180°

square

Polygons!

N sides , int. angle of N-gon:(n - 2) × 180°

Problem involving regular polygons with unknown no. of sides Finding no. of sides using exterior angles of n-sided polygon Sum of ext. angles=360° Given size of each ext. angle: 24° n=360°/24°=15

Finding no. of sides in regular polygon if interior angle is given as°162° (n-2)x180°/n= 162° (n-2)x180°=162° x n 180n-162n=360 18n=360 n=20

Sum on int. angles in a decagon Decagon:10 sides Sum of int angles: (nx2)× 180°

Pentagon: 5 sides , 3 triangles formed Hexagon: 6 sides , 4 Triangles formed Heptagon: 7 sides , 5 triangles formed Octagon: 8 sides , 6 triangles formed Nonagon: 9 sides, Decagon: 10 sides

exterior angle of a polygon = 360 ÷ number of sides.

sum of interior angles Pentagon:540° Hexagon: 720° Heptagon: 900° Octagon: 1080° Nonagon: 1260° Decagon: 1440° Formula :int. angle=(n - 2) × 180°

Triangles

Appropriate labels to add in questions involving triangles: (ext. ∠ of △ ) (∠ sum of △) In questions involving exterior angle of triangle which are formed by parallel line and transversal: (Vert. Opp. ∠s) and (corr. ∠s, BC//DE still applies

x°+32°+47°=180°( ∠ sum of △)

scalene

0 equal sides

isosceles

At least 2 equal sides

Usable terms: (base ∠s of Isos △ABD

Acute, obtuse and right angles triangles

Right angle: One angle is 90°

Obtuse : One angle more than 90°

Acute: all angles lesser than 90°

Equilateral triangles

All angles are 60° , all sides equal length