"Pay attention to the exterior angles of the triangle" Proof PPT courseware 4

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"Pay attention to the exterior angles of the triangle" Proof PPT courseware 4

Self-study tips

As shown in the figure: ∠1 is an exterior angle of △ABC

1. What are the characteristics of the vertices and edges of ∠1?

2. Can you draw all the exterior angles of △ABC?

3. What is the relationship between ∠1 and other angles in the figure?

Can you prove your conclusion?

Corollary to the sum of angles theorem of a triangle:

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

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

Consolidation exercises

1. As shown in the figure, D is a point on the extension line of BC, ∠ ACD=100 degrees, ∠ B=55 degrees.

Find the degrees of ∠A and ∠ACB.

2. As shown in the figure, it is known that in a pentagon, prove: ∠ A + ∠ B+∠C+ ∠D +∠E=180°

Prove: ∵∠1 is an exterior angle of △CGE.

∴∠1=∠C+∠E

∵∠2 is an exterior angle of △BFD

∴∠2=∠B+∠D

∵∠1+∠2+∠A =180°

∴∠A+∠B+∠D+∠C+∠E =180°

The exterior angle ∠1 has the following three characteristics:

1. The vertex of ∠1 is a vertex of △ABC;

2. One side of ∠1 is one side of △ABC;

3. The other side of ∠1 is the extension line of one side of △ABC.

self-study report

As shown in the figure, ∠1 has the following relationship with other angles in the figure:

1. ∠1+∠4=180°

2. ∠1=∠2 +∠3

3. ∠1>∠2, ∠1 >∠３

Prove ∵ ∠ 2+ ∠３+ ∠４=180 °

∠1+∠４=180°

∴∠1=∠2 +∠３

∴∠1 >∠2, ∠1 >∠３

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For more information about the PPT courseware "Prove Concern about the Exterior Angle of a Triangle", please click the Prove ppt Concern about the Exterior Angle of a Triangle ppt tag.

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"Focus on the exterior angles of a triangle" Proof PPT Courseware 2:

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Update Time: 2024-09-07

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