"Sum of Interior Angle Theorem of a Triangle" Proof of Parallel Lines PPT Courseware

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"Sum of Interior Angles Theorem of a Triangle" Proof of Parallel Lines PPT Courseware

Axioms: The principles that people have summarized in long-term practice and are generally accepted as correct are called axioms.

1. Straight line axiom: Two points determine a straight line.

2. Line segment axiom: The shortest line segment between two points.

3. Parallel Axiom: There is and is only one straight line parallel to the known straight line through a point outside the straight line.

4. Vertical Axiom: There is and is only one straight line perpendicular to a known straight line through a point.

5. Determination axiom of parallel lines: If two straight lines are intercepted by a third straight line, if the angles are equal, then the two straight lines are parallel.

6. Judgment axioms for triangle congruence: SAS ASA SSS.

7. Axioms of properties of congruent triangles: Corresponding angles are equal and corresponding sides are equal.

8: The relevant properties of equations and inequalities can be regarded as axioms

In an equation or inequality, a quantity can be replaced by its equivalent. For example, if a=b, b=c, then a=c, this property is also regarded as an axiom and is called "equivalent substitution".

General steps for proof:

Step 1: Analyze conditions, conclusions, and draw graphs.

Step 2: Based on the conditions, conclusions, and combined graphics, write down what is known and verify.

Step 3: After analysis, find a way to deduce the verification from what is known.

Step 4: Combine the graphics and write the proof process.

Here, for the purpose of proof, the lines added on the original graphics are called auxiliary lines. In plane geometry, auxiliary lines are usually drawn as dashed lines. Pay attention to the location, name and nature of the added auxiliary lines.

Summary of ideas:

In order to prove that the sum of the three interior angles of a triangle is 180°, the transformation idea is usually applied. Converted to:

A straight angle or using two straight lines parallel to each other, and the interior angles on the same side are complementary

What did you learn in this lesson?

1. Theorem of the sum of the interior angles of a triangle: The sum of the three interior angles of a triangle is equal to 180°

2. Through thinking, exploration, and summarizing the theorem of the sum of the interior angles of a triangle, we 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: the sum of the interior angles of a straight angle or two straight lines parallel to the same side is equal to 180°.

3. In the theorem proof of the sum of the interior angles of a triangle, the essence of adding auxiliary lines is to move the angles through parallel lines.

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For more information about the PPT courseware "Proof of Interior Angles of Triangles and Parallel Lines Theorem", please click on the Proof of Interior Angles of Triangles and Parallel Lines Theorem ppt ppt tag.

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

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"Sum of Interior Angles Theorem of a Triangle" PPT courseware:

"The Sum of the Interior Angles of a Triangle Theorem" PPT courseware preview check 1. What are the sum of the interior angles of a triangle 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..

"Proof of the Sum of the Interior Angle Theorem of a Triangle" Proof PPT Courseware 4:

"Proof of the sum of the interior angles of a triangle theorem" Proof PPT courseware 4 [Learning objectives]: 1. Proof of the sum of the interior angles of a triangle theorem. 2. Master the theorem of the sum of the interior angles of a triangle, and initially learn to use auxiliary lines to prove problems [important and difficult points in learning] 1. focus: triangles The sum of interior angles theorem...

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Update Time: 2024-11-14

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