"Determination of Isosceles Triangle" Proof PPT Courseware

"Determination of Isosceles Triangle" Proof PPT Courseware

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"Determination of Isosceles Triangle" Proof PPT Courseware

Draw some line segments (such as angle bisectors, midlines, heights, etc.) in the isosceles triangle.

Can you find some of these equal segments?

Can you spot some of these equal angles?

Can you prove the findings?

1. Known: As shown in the figure, in △ABC,

(1) If ∠ABD=∠ABC/2, ∠ACE=∠ACB/2, then BD=CE? What if ∠ABD=∠ABC/3, ∠ACE=∠ACB/3? From this you can get a What conclusion?

(2) If AD=AC/2, AE=AB/2, then BD=CE? What if AD=AC/3, AE=AB/3? What conclusion can you draw from this?

(3) Can you prove the conclusion you obtained?

Here is a mathematical thinking method that summarizes general conclusions from special conclusions.

2. We have already proved that "equilateral angles correspond to equilateral angles", but conversely, "equilateral angles correspond to equilateral sides"?

That is, is a triangle with two equal angles an isosceles triangle?

Known: As shown in the figure, in △ABC, ∠B = ∠C.

Prove: AB=AC.

Analysis: To prove that AB=AC, as long as the two triangles where AB and AC are located are congruent, it is enough.

How do you think? Share your approach with your peers.

For example: draw the midline on side BC; draw the bisector of ∠A or draw the height of side BC.

theorem:

A triangle with two equal angles is an isosceles triangle (equal angles and equal sides).

In △ABC

∵∠B=∠C (known),

∴AB=AC (equiangular opposite sides).

General steps to prove 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, and arriving at results that are inconsistent with definitions, axioms, proven theorems or known conditions;

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

Teacher suggestion:

Proof by contradiction is an important mathematical proof method. It often has unexpected effects when solving certain problems.

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

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"Determination of Isosceles Triangle" Proof PPT Courseware 2:

"Determination of Isosceles Triangle" Proof PPT Courseware 2 General steps to prove a proposition: (1) Understand the meaning of the question: distinguish the conditions (known) and conclusion of the proposition (prove); (2) Draw the figure according to the meaning of the question; (3) Use symbolic language to write what is known and verified based on graphics; (4) Analyze and explore the meaning of the question.

"Determination of Isosceles Triangle" Axisymmetric PPT Courseware:

"Determination of Isosceles Triangle" Axis Symmetry PPT Courseware Determination of Isosceles Triangle: If there are two angles in a triangle that are equal, then the sides opposite the two angles are also equal. (Equal angles versus equal sides) Analysis: Obviously the length of the rope CD and CE are equal, the problem is actually known..

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