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Authoritative PPT Summary
"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.
"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...
"Focus on the exterior angles of a triangle" proof PPT courseware:
"Focus on the Exterior Angle of a Triangle" proves the PPT courseware exploration and thinking 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; 12; 13; 1=2+3. Can prove What is your conclusion? Proof: ∵2+3+4=180 (Sum of interior angles of a triangle theorem)..