"Sum of Interior Angles Theorem of a Triangle" Proof of Parallel Lines PPT (Lesson 2)

Description

"The Sum of the Interior Angles of a Triangle Theorem" Proof of Parallel Lines PPT (Lesson 2), 36 pages in total.

Part One: Learning Objectives

1. Understand and master the definition of exterior angles of a triangle. (emphasis)

2. Master the properties of the exterior angles of a triangle and use the properties of the exterior angles to perform simple proofs and calculations. (difficulty)

Sum of interior angles theorem of a triangle PPT, part 2 content: teaching a new lesson

The concept of exterior angles of a triangle

definition

As shown in the figure, extend one side BC of △ABC to get ∠ACD. Like this, the angle formed by one side of the triangle and the extension of the other side is called the exterior angle of the triangle.

Summary

①The vertex of the angle is the vertex of the triangle;

②One side of the angle is one side of the triangle;

③The other side is the extension of one side of the triangle.

Properties of exterior angles of triangles

Question 1 As shown in the figure, what is the relationship between the exterior angle ∠BCD of △ABC and its adjacent interior angle ∠ACB?

In conclusion

Properties of exterior angles of triangles:

Property 1: An exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles.

Property 2: An exterior angle of a triangle is greater than any interior angle that is not adjacent to it.

Sum of interior angles theorem of triangles PPT, part 3: practice in class

1. Judge whether the following propositions are true or false.

(1) The sum of the exterior angles of a triangle refers to the sum of all exterior angles of the triangle. ( )

(2) The sum of the exterior angles of a triangle is equal to twice the sum of its interior angles. ( )

(3) An exterior angle of a triangle is equal to the sum of the two interior angles. ( )

(4) An exterior angle of a triangle is equal to the sum of two interior angles that are not adjacent to it. ( )

(5) An exterior angle of a triangle is greater than any interior angle. ( )

(6) An interior angle of a triangle is smaller than any exterior angle that is not adjacent to it. ( )

2. As shown in the figure, AB//CD, ∠A＝37°, ∠C＝63°, then ∠F equals ( )

Sum of interior angles theorem of triangles PPT, Part 4 content: Class summary

definition

One side of the angle must be one side of the triangle, and the other side must be the extension of the other side of the triangle.

nature

1. The exterior angle of a triangle is equal to the sum of its two interior angles that are not adjacent to it.

2. The exterior angle of a triangle is greater than any interior angle that is not adjacent to it.

The sum of the exterior angles of a triangle

The sum of the exterior angles of a triangle is 360°

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Update Time: 2024-11-12

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