| Category | Format | Size |
|---|---|---|
| Beijing Normal University Ninth Grade First Volume Mathematics | pptx | 6 MB |
"Determination of Equilateral Triangle" Proof PPT Courseware
Description
"Determination of Equilateral Triangle" Proof PPT Courseware
What conditions must be met for a triangle to become an equilateral triangle?
What conditions must be met for an isosceles triangle to become an equilateral triangle?
Do you think an isosceles triangle with an angle of 600 is an equilateral triangle? Can you prove your conclusion?
Share with your peers what you did in the process of exploring ideas.
Theorem: An isosceles triangle with an angle of 600 is an equilateral triangle.
Known: As shown in the figure, in △ABC, AB=AC, ∠B=600.
Prove: △ABC is an equilateral triangle.
Proof: ∵AB=AC, ∠B=600 (known),
∴∠C=∠B=600. (Equal sides correspond to equal angles).
∴∠A=600 (Sum of interior angles of a triangle theorem).
∴∠A=∠B (equality property).
∴ AC=CB (equiangular opposite sides).
∴AB=BC=AC (equality property).
∴ △ABC is an equilateral triangle (equilateral triangle meaning).
Right triangle with 30° angle
1. Known: As shown in the figure, in △ABC, ∠ACB=900, ∠A=300, CD⊥AB is in D. Verify: BD=AB/4.
Analysis: Because ∠A=300, so BC=AB/2. To prove BD=AB/4, as long as BD=BC/2 can be made, at this time, if ∠BCD=300. And by "double vertical Triangle" can be obtained.
2. Known: As shown in the figure, points P and Q are on BC, and BP=AP=AQ=QC=a, ∠PAQ=600, AH⊥BC is on H.
(1) Verify: AB=AC;
(2) Try to mark the degrees of each angle in the picture;
(3) Find the length of each line segment in the figure and explain the reason.
Endless aftertaste
Determination of equilateral triangle:
Theorem: An isosceles triangle with an angle of 600 is an equilateral triangle.
Theorem: A triangle with three equal angles is an equilateral triangle.
Properties of special right triangles:
Theorem: In a right triangle, if there is an acute angle equal to 300, then the right side it opposes is equal to half of the hypotenuse.
Theorem: In a right triangle, if a right-angled side is equal to half the hypotenuse, then the acute angle it subtends is equal to 300.
Teacher reminds: Do you still know you by proof by contradiction?
Keywords: Proof courseware, Judgment of Equilateral Triangle courseware, Beijing Normal University Edition Ninth Grade Mathematics Volume 1 PPT Courseware, Ninth Grade Mathematics Slide Courseware Download, Proof PPT Courseware Download, Judgment of Equilateral Triangle PPT Courseware Download, .ppt format
For more information about the PPT courseware "Proving the Determination of Equilateral Triangles", please click on the Prove ppt Determination of Equilateral Triangles ppt tag.
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Update Time: 2024-07-04
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