Using geometric notation Slideshow 42, Mathematics Mr Richard Sasaki, Room 307

Objectives Understand some extra notation for shape construction Use such notation for explanation of shape properties

Chapter 5 Chapter 5 is mostly about proof. For this reason, we will be proving certain properties in triangles and parallelograms. We will need some new notation for this.

PHRASES F Line AB is _________ to line CD and _______________ to line FE. parallel C D perpendicular A B E Lines of non-infinite lengths we call ______________. line segments

Notation - Review ∠𝐴𝐵𝐶=∠𝑋𝑌𝑍 𝐴𝐵=𝑋𝑌 ∆𝐴𝐵𝐶≅∆𝑋𝑌𝑍 ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍 Angle ABC is equal to angle XYZ. 𝐴𝐵=𝑋𝑌 Distance AB is the same as distance XY. ∆𝐴𝐵𝐶≅∆𝑋𝑌𝑍 Triangle ABC is congruent to triangle XYZ. ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍 Triangle ABC is similar to triangle XYZ.

Notation 𝐴𝐵 ∥ 𝑋𝑌 𝐴𝐵 ⊥ 𝑋𝑌 𝐴𝐵 = 𝑋𝑌 𝐴𝐵 Line segment AB is parallel to line segment XY. 𝐴𝐵 ∥ 𝑋𝑌 Line segment AB is perpendicular to line segment XY. 𝐴𝐵 ⊥ 𝑋𝑌 Line segment AB is the same length as line segment XY. 𝐴𝐵 = 𝑋𝑌 A line of infinite length passes through A and B. 𝐴𝐵

Answers 𝐴𝐵 , 𝑋𝑌 , 𝐴𝐵 ∥ 𝑋𝑌 , 𝐴𝐵 ⊥ 𝑋𝑌 𝐴𝐵 intersects 𝑋𝑌 𝐴𝐵 , 𝑋𝑌 , 𝐴𝐵 ∥ 𝑋𝑌 , 𝐴𝐵 ⊥ 𝑋𝑌 𝐴𝐵 intersects 𝑋𝑌 Parallel lines never touch so they can’t intersect. Therefore they can’t be perpendicular. S E T D U G R F A D C B

Line types Line passing through A and B Line segment from A to B Ray from A, passing through B B