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CHAPTER ELEVEN MATH 1A POWERPOINT PRESENTATION GEOMETRY

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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

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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

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INTERSECTING LINES

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VERTEX/ANGLE/RAY

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PROTRACTOR

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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

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ADJACENT ANGLES

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VERTICAL ANGLES

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Acute/Obtuse

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Complementary/Supplementary

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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

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External Angles External Angles The external angle is angle w

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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.

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Tick Marks

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TYPES OF TRIANGLES

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Other Triangles

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

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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.

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Examples of Congruence SAS

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Angle-Side-Angle Congruence ASA

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Side-Side-Side Congruence SSS

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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:

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

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What Quadrilaterals Look Like

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

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Geometry – Awesome!!!!

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