Category | Format | Size |
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Beijing Normal University Ninth Grade First Volume Mathematics | pptx | 6 MB |
Description
"Can you prove them" Proof PPT courseware 4
Properties of isosceles triangle:
Theorem: The two base angles of an isosceles triangle are equal
Corollary: The bisector of the vertex of an isosceles triangle, the midline on the base, and the height line on the base coincide with each other (three lines merge into one)
Conclusion 1: The three angles of an equilateral triangle are equal, and each angle is equal to 60°
Conclusion 2: The angle between the altitude on the waist of an isosceles triangle and the base is equal to half of the vertex angle.
Conclusion 3: The sum of the distances from any point on the base of an isosceles triangle to the two waists is equal to the height of one waist
Conclusion 4: The bisectors of the two base angles of an isosceles triangle are equal.
Conclusion 5: The altitude and midline of the two sides of an isosceles triangle are equal.
Determination theorem: A triangle with two equal angles is an isosceles triangle. Abbreviation: equiangular and equilateral sides.
think about it
(1) When an isosceles triangle meets what conditions, it becomes an equilateral triangle?
(2) Do you think an isosceles triangle with an angle equal to 600 is an equilateral triangle? Can you prove your conclusion? Share your proof ideas with your peers.
Theorem: An isosceles triangle with an angle of 60° 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).
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For more information about the PPT courseware "Prove Can You Prove Them", please click the Prove ppt Can You Prove Them ppt tag.
"Can you prove them" Proof PPT courseware 3:
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"Can you prove them" Proof PPT courseware 2:
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Update Time: 2024-07-01
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