CHAPTER ELEVEN MATH 1A POWERPOINT PRESENTATION GEOMETRY

LEARNING TARGETS AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: MEASURE AND CLASSIFY ANGLES NAME AND CLASSIFY TRIANGLES FIND THE MEASURE OF ANGLES IN TRIANGLES IDENTIFY QUADRILATERALS DETERMIN DEGREES IN POLYGONS

VOCABULARY INTERSECTION: THE POINT WHERE TWO LINES CROSS IN A FIGURE RAY: PART OF A LINE THAT HAS ONE ENDPOINT AND EXTENDS INDEFINIETLY IN ONE DIRECTION VERTEX: A COMMON POINT TO BOTH SIDES OF AN ANGLE PROTRACTOR: A TOOL USED TO DRAW AND MEASURE ANGLES

INTERSECTING LINES

VERTEX/ANGLE/RAY

PROTRACTOR

Identifying & Classifying Angles Adjacent: two angles with the same vertex that share a side Vertical: angles formed by intersecting lines Acute: an angle < 90⁰ Obtuse: an angle > 90⁰ Complementary Angles = 90⁰ Supplementary Angles = 180⁰

ADJACENT ANGLES

VERTICAL ANGLES

Acute/Obtuse

Complementary/Supplementary

Internal/External Angles Internal Angles: formed by extending one side of a polygon at any vertex Internal Angles: any angle within a polygon Triangle – 180⁰ of internal angles Quadrilateral (4 sided figures) – 360⁰ of internal angles Pentagon – 540⁰ of internal angles Hexagon – 720⁰ of internal angles Octagon – 1080⁰ of internal angles

External Angles External Angles The external angle is angle w

Naming Triangles Tick – a short line used to mark sides in geometry Acute Triangle – no angles >90⁰ Obtuse Triangle – one angle >90⁰ Equiangular Triangle – all angles equal Right Triangle - one angle exactly 90⁰ When you name triangles this way, you are naming them by their angles.

Tick Marks

TYPES OF TRIANGLES

Other Triangles

Congruence Congruent Shapes – are alike in every detail. Congruent Triangles:

Three Theorems to Prove Congruence Angle-Side-Angle: (ASA) – two like angles, one like side. Side-Side-Side: (SSS) – all sides are alike Side-Angle-Side: (SAS) – two like sides, one like angle. These theorems are proved by examining the ticks in the two triangles.

Examples of Congruence SAS

Angle-Side-Angle Congruence ASA

Side-Side-Side Congruence SSS

Similar Shapes Similar: figures that have the same shape but not the same size. Corresponding Angles: interior or exterior angles in figures with the same proportions, and shape, but not the same size:

Quadrilaterals Quadrialterals: shapes with 4 sides: Square and Rectangle Parallelogram and Rhombus Kite Trapezoid All Internal Angles = 360⁰

What Quadrilaterals Look Like

Diagonals Diagonals – are line segments connecting two vertices (points) that are not next to each other.

Geometry – Awesome!!!!