"Sum of Interior Angle Theorem of a Triangle" PPT courseware

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"Sum of Interior Angle Theorem of a Triangle" PPT courseware

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1. What are the triangle interior angle sum theorem and its corollaries 1 and 2?

2. What is inference? Can the corollary be used as a theorem?

3. What is an auxiliary line? What lines are usually drawn as auxiliary lines?

Question 1

Triangle Blue and Triangle Red met, and Blue said ostentatiously: "My volume is larger than yours, so the sum of my internal angles is also larger than yours!" Red said unconvinced: "That's hard to say, you can measure it yourself! "

Lan used a protractor to measure the sum of his interior angles and stopped talking!

Students, do you know the reason?

Question 2.

There are three interior angles in a right triangle. Usually, the three brothers are very united. But one day, the second child suddenly became unhappy and lost his temper. He pointed at the eldest child and said: "Why do you have the greatest degree? I want to fight with you too." The same size!" "No!" said the eldest brother: "This is impossible, otherwise, our family will no longer be able to surround it..." "Why?" The second eldest child was puzzled.

Students, do you know the reason?

learning target

1. Use jigsaw puzzle to verify the sum of the interior angles of a triangle.

2. Be able to understand and master the proof process of the sum of interior angles theorem of a triangle.

3. Be able to flexibly apply the triangle interior angle sum theorem to perform simple calculations and reasoning proofs.

The sum of the three interior angles of a triangle is 180°

What are the conditions? What is the conclusion?

Condition: There are three angles that are the three interior angles of a triangle

Conclusion: Their sum is equal to 180°

Can you draw a graph combining conditions and conclusions? Give it a try

Question: Is there any way to get 180°

1. The measure of a straight angle is 180°

2. If two straight lines are parallel, the sum of interior angles on the same side is 180°

3. The sum of adjacent supplementary angles is 180°

Can you think of a way to prove it from the process of fighting just now?

Explore together 1

Known: As shown in the figure, △ABC.

Prove: ∠A+∠B+∠C=1800.

Analysis: Extend BC to D, and make ∠A = ∠1 through point C. In this way, CE∥AB is equivalent to moving ∠A to the position of ∠1 and moving ∠B to the position of ∠2.

Proof: Draw the extension line CD of BC and draw ∠A= ∠1 through point C, then

CE∥AB( )

∴ ∠2= ∠B( ).

And ∵∠1+∠2+∠3=1800 ( ),

∴ ∠A+∠B+∠ACB=1800 ( ).

Do you have any other ways to prove the triangle angle sum theorem?

Theorem: The sum of the three interior angles of a triangle is 180°

discuss

Can there be two right angles in a triangle?

Can a triangle have two obtuse angles?

Can all three interior angles be less than 60°?

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.

Compliance in court

1. (1) In △ABC, ∠A=35°, ∠B=43°, then ∠C= ＿＿＿.

(2) In △ABC, ∠C=90°, ∠B=50°, then ∠A = ＿＿＿.

(3) In △ABC, ∠A=40°, ∠A=2∠B, then ∠C = ＿＿＿.

2. It is known that in △ABC, ∠B is twice as large as ∠A, and ∠C is 20° larger than ∠A. Find ∠A.

3. It is known that the ratio of the measures of the three interior angles of a triangle is 1:3:5. Find the measures of these three interior angles.

Solution: Suppose the three interior angles are: x, 3x, 5x,

The sum of the interior angles of a triangle is 180°

x+3x+5x=180°

Solve for x=20°

So the three internal angles are 20°, 60°, and 100° respectively.

What did you learn in this lesson? ? ?

1. Knowledge points:

2. Method: ⑴Through thinking, exploring, and summarizing the theorem of the sum of the interior angles of a triangle, and found that to prove that the sum of the three interior angles of a triangle is equal to 180°, it needs to be converted into: ① a straight angle by drawing auxiliary lines; ② two straight lines are parallel and have the same side angles The sum is equal to 180°; ③ adjacent supplementary angles. (2) Use equations or systems of equations to find angles (3) Concentrate scattered angles onto triangles or polygons.

3. Draw inferences from one instance:

4. The location of this part of knowledge in the knowledge system:

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For more information about the "Sum of Interior Angles of Triangles Theorem" PPT courseware, please click the "Sum of Interior Angles of Triangles Theorem" ppt tag.

"Sum of Interior Angle Theorem of a Triangle" PPT courseware 2:

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Update Time: 2024-08-17

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