"Inscribed Circles of Triangles" PPT courseware

Description

"Inscribed Circles of Triangles" PPT courseware

The picture shows a triangular piece of wood. The carpenter wants to cut a circular piece of material from it. How can the area of ​​the cut circle be made as large as possible?

The circle that is tangent to all sides of a triangle is called the inscribed circle of the triangle

A triangle is called a circumscribed triangle of a circle

Example 1: Construct a circle so that it is tangent to all sides of the known triangle.

Known: △ABC (as shown in the picture)

Find a circle that is tangent to all sides of △ABC

Question 1: What is the key to making a circle?

(Determine the center and radius of the circle)

Question 2: How to determine the position of the center of the circle?

(Draw two angle bisectors, and their intersection is the center of the circle)

Question 3: How to determine the radius of the circle after the position of the center of the circle is determined?

(Draw a perpendicular to one side of the triangle through the center of the circle. The length of the perpendicular segment is the radius of the circle)

Question 4: Can a larger circle be cut out of this triangular piece of material?

(No) Any triangle has only one inscribed circle

Known: △ABC (picture)

Find a circle that is tangent to all sides of △ABC

Method: 1. Construct the bisectors BM and CN of ∠ABC and ∠ACB, and the intersection point is I.

2. Draw ID⊥BC through point I, and draw the vertical foot as D.

3. Taking I as the center of the circle and ID as the radius, make ⊙I. ⊙I is the desired circle.

The center of the inscribed circle of a triangle is called the incenter of the triangle

①The center of a triangle is the intersection of the angle bisectors of the triangle

②The distance from the center of the triangle to the three sides is equal

③The center of the triangle must be inside the triangle

Class summary:

1. This lesson starts with practical problems and explores how to find the inscribed circle of a triangle.

2. By analogy with the concepts of the circumcircle of a triangle and the inscribed triangle of a circle, the concepts of the inscribed circle of a triangle and the circumscribed triangle of a circle are derived, and the concepts of the inscribed circle of a polygon and the circumscribed polygon of a circle are introduced.

3. When studying, you must clarify the meaning of "connection" and "cut", and clarify the difference between "inner heart" and "outer heart".

4. When using the inner properties of triangles to solve problems, we should pay attention to the application of overall thinking. When solving practical problems, we should pay attention to converting practical problems into mathematical problems.

Keywords: teaching courseware of inscribed circles of triangles, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, download of inscribed circles of triangles PPT courseware, .PPT format;

For more information about the "Inscribed Circles of Triangles" PPT courseware, please click the Inscribed Circles of Triangles ppt tab.

"Inscribed Circles of Triangles" PPT courseware 3:

"Inscribed Circle of a Triangle" PPT Courseware 3 Review Definition of tangent length: Draw the tangent of the circle through a point outside the circle. The length of the line segment between this point and the tangent point is called the tangent length from this point to the circle. Tangent length theorem: Two tangents to a circle can be drawn from a point outside the circle, and their...

"Inscribed Circles of Triangles" PPT Courseware 2:

"Inscribed Circles of Triangles" PPT Courseware 2 As shown in the picture, the carpenter wants to cut a circular piece from a triangular piece of wood. How can he make the area of ​​the cut circle as large as possible? Construct a circle so that it is tangent to all sides of the known triangle. Given: △ABC (as shown in the figure). Find the...

File Info

Update Time: 2024-10-05

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

Preview