chapter eleven math 1a powerpoint presentation geometry
TRANSCRIPT
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!!!!