"Can you prove them" Proof PPT courseware 2

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"Can you prove them" Proof PPT courseware 2

Definition A triangle with two equal sides is called an isosceles triangle;

Property theorem: The two base angles of an isosceles triangle are equal. Abbreviation: Equilateral equal angles.

Corollary of the property theorem: The bisector of the vertex angle of an isosceles triangle, the midline on the base, and the height on the base coincide with each other.

What other important properties does an isosceles triangle have?

In addition to using definitions to determine whether a triangle is an isosceles triangle, are there any simple methods to determine whether a triangle is an isosceles triangle?

draw a picture

First draw an isosceles triangle, and then make some line segments in the isosceles triangle (such as angle bisector, midline, altitude line). Can you find some of the equal line segments?

Can you prove your conclusion?

There is only one bisector, middle line, and high line of the vertex angle and cannot be compared;

The two bisectors of a base angle are equal;

The midlines on both waists are equal;

The high lines on both waists are equal.

Assuming AB=AC, then according to the "equal angles and equal sides" theorem, we can get ∠B = ∠C.

But the known condition is ∠B≠∠C.

"∠B=∠C" contradicts "∠B≠∠C", therefore, AB≠AC.

When Xiao Ming is proving, he first assumes that the conclusion of the proposition is not established, and then derives results that are inconsistent with definitions, axioms, proven theorems or known conditions, thereby proving that the conclusion must be established. This method of proof is called proof by contradiction.

Proof by contradiction is an important mathematical proof method.

It often has unexpected effects in solving certain problems.

You need to make a new friend, "Evidence by Contradiction"!

General steps to prove a question using proof by contradiction

1. Assumption: First assume that the conclusion of the proposition is not true;

2. Reductio ad absurdum: Starting from this hypothesis, applying correct inference methods, we arrive at results that are inconsistent with definitions, axioms, proven theorems or known conditions;

3. Conclusion: The hypothesis is determined to be incorrect based on the contradictory results, thus confirming that the conclusion of the proposition is correct.

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"Can you prove them" Proof PPT courseware 4:

"Can you prove them" Proof PPT courseware 4 Properties of an isosceles triangle: Theorem: The two base angles of an isosceles triangle are equal Corollary: The bisector of the vertex angle of an isosceles triangle, the midline on the base, and the height on the base The lines coincide with each other (three lines merge into one) Conclusion 1: Equilateral triangle..

"Can you prove them" Proof PPT courseware 3:

"Can you prove them?" Proof PPT courseware 3 Judgment axiom: Two triangles corresponding to three sides are congruent (SSS). Two sides and their angles correspond to two triangles congruent (SAS). Two angles and their angles are congruent (SAS). Two triangles whose sides correspond to are congruent (ASA). You...

"Can you prove them" Proof PPT courseware:

"Can You Prove Them" Proof PPT courseware 1. Review and consolidate the relevant content of proof (1) last semester; 2. Understand the contents of several axioms that are the basis of proof, and master the basic steps and writing format of proof. 3. Experience the process of exploration-discovery-conjecture-prove...

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Update Time: 2024-09-18

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