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EdrawMindChapter 11 Triangle Mind Map
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Chapter 11 Triangle Mind Map
This is a mind map about triangles, including line segments related to triangles, angles related to triangles, polygons and their interior angle sums, etc. I hope it will be helpful to you!
Edited at 2023-11-04 14:54:06- bacteria
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Chapter 11 Triangle Mind Map
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
- Reproductive development of animals
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
- Recommended to you
- Outline
Chapter 11 triangle
11.1 Line segments related to triangles
Concepts related to triangles
1.Triangle
A figure composed of three line segments that are not on the same straight line and are connected end to end is called a triangle.
2. Sides and angles of triangles
The three line segments that make up a triangle are the three sides of the triangle. The angle formed by two adjacent sides is called the interior angle of the triangle, or simply the angle of the triangle.
3. Representation method
Vertex: represented by capital letters; Sides: Indicated by lowercase letters.
Classification of triangles
(1) According to the relationship between sides
A triangle with three sides that are not equal
isosceles triangle
Isosceles triangle (triangle with two equal sides) whose base and waist are not equal
Equilateral triangle (a triangle with all three sides equal)
(2) According to the angle relationship
right triangle
obtuse triangle
Acute triangle
trilateral relations
1. The sum of two sides of a triangle is greater than the third side
2. The difference between the two sides of a triangle is less than the third side
Height, median and angle bisector of a triangle
1.Height of triangle
Draw a vertical line from a vertex of a triangle to the side opposite it. The line segment between the vertex and the vertical foot is called the height of the triangle.
2. The midline of the triangle
The line segment connecting a vertex of a triangle to the midpoint of the side opposite it is called the midline of a triangle
3. Angle bisectors of triangles
The angle bisector of an angle of a triangle intersects the opposite side of the angle
4.Intersection point of three lines
(1) The three midlines are all inside the triangle - the center of gravity
(2) The three angle bisectors are all inside the triangle - the center
(3) Be sincere
Acute triangle - all three heights are inside the triangle
Right triangle - two heights coincide with two right sides
Obtuse triangle - two heights are outside the triangle
triangle stability
Triangles are stable, but quadrilaterals are not.
angles related to triangles
interior angles of triangle
1.The sum of the interior angles of a triangle
(1) Theorem: The sum of the interior angles of a triangle is equal to 180°
(2) Form: In triangle ABC, ∠A ∠B ∠C=180°
(3) Proof method: cut into square angles; make parallel lines.
2. Properties and judgment of right triangles
The symbol “Rt△
(1) Properties: The two acute angles of a right triangle are complementary to each other
(2) Decision: A triangle with two complementary angles is a right triangle
exterior angle of triangle
1. Definition: The angle formed by one side of a triangle and the extension of the other side is called the exterior angle of the triangle.
2. Property: The exterior angle of a triangle is equal to the sum of its two interior angles that are not adjacent to it.
Polygon and its interior angle sum
Polygons and related concepts
1.Polygon
In a plane, a closed figure composed of some line segments connected end to end is called a polygon.
2. Interior angles of polygons
The angle formed by two adjacent sides of a polygon
3.Exterior angle of polygon
The angle formed by a side of a polygon and the extension of its adjacent side is called the exterior angle of the polygon.
4. Diagonals of polygons
The line segment connecting two non-adjacent vertices of a polygon is called the diagonal of the polygon. [Number of entries: n(n-3)\2]
5. Regular polygon
A polygon with all angles equal and all sides equal is called a regular polygon
angle
1. The sum of the interior angles of a polygon - (n-2)∙180°
2. The sum of the exterior angles of a polygon - 360°