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!!!!