Geometry 7 Chapter 3

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Math 7 Chapter 3 Lesson 6: Properties of the three bisectors of a triangle

Math 7 Chapter 3 Lesson 6: Properties of the three bisectors of a triangle 1. Summary of theory 1.1. The bisector of the triangle In triangle ABC, the bisector of angle A intersects side BC at point M. The line segment AM is called the bisector of triangle ABC. The line AM is also called …

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Math 7 Chapter 3 Lesson 7: Properties of the perpendicular bisector of a line segment

Math 7 Chapter 3 Lesson 7: Properties of the perpendicular bisector of a line segment 1. Summary of theory 1.1. Properties of points on the perpendicular Theorem 1: (Forward Theorem): A point on the perpendicular bisector of a line segment is equidistant from the two endpoints of that segment. Eg: Since point M lies on …

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Math 7 Chapter 3 Lesson 8: Properties of the three perpendicular bisectors of a triangle

Math 7 Chapter 3 Lesson 8: Properties of the three perpendicular bisectors of a triangle 1. Summary of theory 1.1. The perpendicular bisector of the triangle In a triangle, the perpendicular bisector of one side is called a perpendicular bisector of that triangle. – Each triangle has three perpendicular bisectors. Comment: In an isosceles triangle, …

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Math 7 Chapter 3 Lesson 9: Properties of the three altitudes of a triangle

Math 7 Chapter 3 Lesson 9: Properties of the three altitudes of a triangle 1. Summary of theory 1.1. Altitude of the triangle. In a triangle, the perpendicular segment from a vertex to the line containing the opposite side is called the altitude of that triangle. Eg: The line segment AI is an altitude of …

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Math 7 Chapter 3 Lesson 5: The property of the bisector of an angle

Math 7 Chapter 3 Lesson 5: The property of the bisector of an angle 1. Summary of theory 1.1. Theorem 1 (forward theorem) A point on the bisector of an angle is equidistant from the sides of that angle. Eg: We have: 1.2. Theorem 2 (inverse theorem) A point inside an angle and equidistant from …

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Math 7 Chapter 3 Lesson 1: The relationship between the angle and the opposite side in a triangle

Math 7 Chapter 3 Lesson 1: The relationship between the angle and the opposite side in a triangle 1. Summary of theory Theorem 1: In a triangle, the angle opposite the larger side is the larger angle. Example 1: Triangle ABC if AC > AB then (widehat B > widehat C) Theorem 2: In a …

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Math 7 Chapter 3 Lesson 2: Relationship between perpendiculars and oblique lines, oblique lines and projections

Math 7 Chapter 3 Lesson 2: Relationship between perpendiculars and oblique lines, oblique lines and projections 1. Summary of theory 1.1. Perpendicular line, oblique line, projection of oblique line. From point A not on line d, draw a line perpendicular to d at H. Take any point B on line d other than point H. …

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Math 7 Chapter 3 Lesson 3: Relationship between the three sides of a triangle Triangle inequality

Math 7 Chapter 3 Lesson 3: Relationship between the three sides of a triangle Triangle inequality 1. Summary of theory 1.1. Triangle inequality Theorem: In a triangle, the sum of the lengths of any two sides is always less than the length of the other side. Eg: Given triangle ABC, we have the following inequalities: …

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