| Category | Format | Size |
|---|---|---|
| Beijing Normal University Ninth Grade First Volume Mathematics | pptx | 6 MB |
"Right Triangle" Proof PPT Courseware
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"Right Triangle" Proof PPT Courseware
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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 one angle of 60° is an equilateral triangle? Can you prove your conclusion?
Theorem: An isosceles triangle with an angle of 600 is an equilateral triangle.
Known: As shown in the figure, in △ABC, AB=AC, ∠B=60°.
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).
Determination of equilateral triangle:
Theorem: An isosceles triangle with an angle of 60° 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 30°, then the right-angled 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 30°.
Teacher reminds: Do you still know you by proof by contradiction?
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"Application of Solving Right Triangles" PPT Courseware 2:
"Applications of Solving Right Triangles" PPT Courseware 2 1. Among the angles formed by the line of sight and the horizontal line, the line of sight on the ______ side of the horizontal line is called the elevation angle, and the line of sight on the ______ side of the horizontal line is called the depression angle. 2. As shown in the figure, the ratio hl of the vertical height h of the slope to ___________ is called...
"Solving Right Triangles" PPT Courseware 2:
"Solving Right Triangles" PPT Courseware 2 There are four basic types of right-angled triangles: (1) The hypotenuse and the right-angled side are known; (2) The hypotenuse and an acute angle are known; (3) The hypotenuse and an acute angle are known; ( 4) Given a right angled side and an acute angle, the solution steps are as follows: 1. (3 points)..
"Determination of Congruence of Right Triangles" PPT courseware:
"Determination of Congruence of Right Triangles" PPT Courseware Learning Objectives 1. Be able to use HL to determine whether two right triangles are congruent. 2. Knowing the hypotenuse and right angle, use a ruler to draw a right triangle. Learning focus: Understand the special method HL of congruent right triangles. And will...
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Update Time: 2024-06-30
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