"Understanding Triangles" Triangle PPT Courseware 6

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"Understanding Triangles" Triangle PPT Courseware 6

Review introduction

1. What kind of figure is called a triangle?

2. What is the relationship between the three sides of a triangle?

3. What is the relationship between the three angles of a triangle?

1. Theorem (1) of the properties of the exterior angles of a triangle:

Any exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles.

2. The unequal relationship theorem of the three sides of a triangle (conditions for whether a triangle can be formed)

1) The sum of any two sides of a triangle is greater than the third side

2) The difference between any two sides of a triangle is less than the third side

3) The difference between the other two sides < the third side < the sum of the other two sides

Review the past and learn the new

1 The sum of the three interior angles of a triangle is equal to _____ degrees.

2 The two acute angles of a right triangle _____.

3 Among the three interior angles of a triangle ( )

A) At least one angle is equal to 90° B) At least one angle is greater than 90°

(C) There may be only one angle less than 90°

(D) It is impossible to all be less than 60°

4 Determine whether the following three line segments a, b, and c can form a triangle.

⑴ a=1cm, b=2cm, c=3cm;

⑵ a=10cm, b=6cm, c=3cm;

⑶ a=2cm, b=10cm, c=11cm;

⑷ a＝1.1cm; b＝8.2cm, c＝9.31cm.

Flexible use:

If the three sides of △ABC are a, b, c, then the result of simplifying |a+b-c|–| b-a-c| is ( ).

(A) 2a-2b (B) 2a+2b+2c

(C) 2b-2c (D) 2a-2c

Discuss

(1) Draw an acute triangle on paper and determine its midline. What method do you have? How many lines does it have?

What is their positional relationship?

(2) What are the midlines of obtuse triangles and right triangles?

give it a try

If you have a piece of tissue paper with a triangle drawn on it, can you think of several ways to draw the bisector of one of its interior angles?

Properties of angle bisectors of triangles

Prepare an acute triangle, an obtuse triangle and a right triangle.

(1) Can you draw the three angle bisectors of these three triangles?

(2) Can you get them by origami?

(3) In each triangle, what is the positional relationship between the three angle bisectors?

Class summary

Through the study of this class, we need to master:

⒈ Definition of angle bisectors and midlines of triangles.

⒉ The three angle bisectors of a triangle intersect at one point, and the three midlines intersect at one point.

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Update Time: 2024-09-07

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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