"Focus on the exterior angles of a triangle" Proof PPT courseware

Description

"Focus on the exterior angles of a triangle" Proof PPT courseware

Explore and think

As shown in the figure. ∠1 is an exterior angle of △ABC. What is the relationship between ∠1 and other angles in the figure?

∠1+∠4=180°;

∠1>∠2;

∠1>∠3;

∠1=∠2+∠3.

Can you prove your conclusion?

Prove: ∵∠2+∠3+∠4=180° (triangle interior angle sum theorem),

∠1+∠4=1800 (the meaning of square angle),

∴∠1= ∠2+∠3. (Equal substitution).

∴ ∠1>∠2,∠1>∠3 (the sum is greater than the part).

Expressed in words:

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

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

Appreciation of examples

Example 1 Known: As shown in the figure, in △ABC, AD bisects the exterior angle ∠EAC, ∠B=∠C.

Prove: AD∥BC.

Prove: ∵∠EAC=∠B+∠C

(An exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles),

∠B=∠C (known),

∴∠C=1/2∠EAC (equality property).

∵ AD bisects ∠EAC (known).

∴∠DAC=1/2∠EAC (definition of angle bisector).

∴∠DAC=∠C (equivalent substitution).

∴ a∥b (the internal offset angles are equal and the two straight lines are parallel).

summary

Corollary to the sum of angles theorem of a triangle:

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

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

application of inference

1 Calculation of angles and proof of angle equality

2 Verify the angle inequality relationship

Keywords: proof teaching courseware, focus on the exterior angles of a triangle teaching courseware, Beijing Normal University edition eighth grade mathematics volume 2 PPT courseware, eighth grade mathematics slide courseware download, proof PPT courseware download, focus on the exterior angles of a triangle PPT courseware download, .ppt format

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.

"Focus on the exterior angles of a triangle" Proof PPT courseware 4:

"Pay attention to the exterior angles of triangles" Proof PPT courseware 4 Self-study tips As shown in the figure: 1 is an exterior angle of △ABC. What are the characteristics of the vertices and sides of 1 and 1? 2. Can you draw all the exterior angles of △ABC? 3. What is the relationship between 1 and other angles in the picture? Can prove your conclusion...

"Focus on the exterior angles of a triangle" Proof PPT Courseware 3:

"Focus on the Exterior Angle of a Triangle" Proof PPT Courseware 3 The sum of the interior angles of a triangle theorem The sum of the interior angles of a triangle theorem The sum of the three interior angles of a triangle is equal to 180. Several variations of A+B+C=180 in △ABC. A+B+C=1800: A=180 (B+C). B=180(A+C). C=180(A+B)...

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

"Focus on the Exterior Angle of a Triangle" Proof PPT Courseware 2 Teaching Objectives 1. Knowledge and Skills: Understand the definition of the exterior angles of a triangle and be able to find the exterior angles of a triangle in any triangle; 2. Process and Method: Experience the variety of questions and multiple questions Use divergent thinking in the process of solving...

File Info

Update Time: 2024-10-16

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

Preview