"Does it have to be a right triangle?" PPT teaching courseware on the Pythagorean Theorem

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"Does it have to be a right triangle?" PPT teaching courseware on the Pythagorean Theorem

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Determination of right triangle

1. As shown in the picture, Xiao Ming’s home has just laid square floor tiles. He connected the three vertices A, B, and C to form a triangle. Then this triangle is (A)

A. Right triangle B. Acute triangle

C. Obtuse triangle D. None of the above

2. If the lengths of the three sides of a triangle are a, b, and c respectively, and satisfy the relationship a2+b2=c2, then the triangle is a right-angled triangle.

3. It is known that the lengths of the three sides of a triangle are 12, 16, and 20 respectively, then the area of ​​this triangle is 96.

4. (Textbook Motif Variation) As shown in the figure, AD⊥BC, the vertical foot is D. It is known that CD=1, AD=2, BD=4,

(1) Find the lengths of AC and AB.

(2) Is △ABC a right triangle? Prove your conclusion.

Knowledge point 2: Pythagorean number

5. Among the following sets of data, which one belongs to Pythagorean number (D)

A.2,3,4 B.4,5,6

C.7,8,9 D.5,12,13

6. There are six wooden sticks with the same thickness. Their lengths are 2, 4, 6, 8, 10, 12 (unit: cm). The lengths of the three wooden sticks connected end to end to form a right triangle are (C)

A.2,4,6 B.4,6,8

C.6,8,10 D.8,10,12

Does it have to be a right triangle? PPT, Part 2: Improvement of Comprehensive Ability

8. △ABC that meets the following conditions is not a right triangle (D)

A.b2-c2=a2

B.a∶b∶c=3∶4∶5

C.∠C=∠A-∠B

D.∠A∠B∠C=9∠12∠15

9. (Original) Observe the following formula:

When n=2, a=2×2=4, b=22-1=3, c=22+1=5;

When n=3, a=2×3=6, b=32-1=8, c=32+1=10;

When n=4, a=2×4=8, b=42-1=15, c=42+1=17;

11. As shown in the figure, there are 9 grid points in the 2×2 square grid. Fixed points A and B have been taken. Pick any point C among the remaining 7 points, so that △ABC is a right triangle. Point C has 4 indivual.

Does it have to be a right triangle? PPT, the third part: Expansion, exploration and breakthrough

16. In △ABC, BC=a, AC=b, AB=c, let c be the longest side. When a2+b2=c2, △ABC is a right triangle; when a2+b2≠c2, use the algebraic formula The size relationship between a2+b2 and c2 can determine the shape of △ABC (classified by angle).

(1) Please explore and judge by drawing pictures: When the three side lengths of △ABC are 6,8,9 respectively, △ABC is an acute triangle; when the three side lengths of △ABC are 6,8,11 respectively, △ ABC is an obtuse triangle.

(2) Based on the above research, Xiao Ming has the following conjecture: "When a2+b2>c2, △ABC is an acute triangle; when a2+b2

When a=3 and b=4, in what range does the longest side c take values? Is △ABC a right-angled triangle, an acute-angled triangle, or an obtuse-angled triangle?

Solution: (2) Because c is the longest side, 3+4=7,

So 4

①If a2+b2>c2, that is, c2<25,0

So when 4

②If a2+b2=c2, that is, c2=25, c=5,

So when c=5, this triangle is a right triangle;

③If a2+b225, c>5,

So when 5

Keywords: Free download of Beijing Normal University edition eighth-grade mathematics PPT courseware for the first volume, must it be a right triangle? PPT download, Pythagorean Theorem PPT download, .PPT format;

For more information about the PPT courseware "Is the Pythagorean Theorem a right-angled triangle?", please click on the PPT tag of "Is the Pythagorean Theorem a right-angled triangle?" PPT courseware.

"Does it have to be a right triangle?" Pythagorean Theorem PPT download:

"Does it have to be a right triangle?" PPT download of the Pythagorean Theorem Part One: Learning Objectives 1. Understand the conditions for determining a right triangle. (Key points) 2. Be able to use Pythagorean to solve simple practical problems. (Difficulty) ... ... ... it must be a right triangle..

"Is it a right triangle?" Pythagorean Theorem PPT:

"Is it Must Be a Right Triangle?" Pythagorean Theorem PPT Part One Content: Review Review: 1. After school, Xiaohong and Xiaoying broke up from school and went home along the southeast and southwest directions respectively. If Xiaohong and Xiaoying were walking The speed is 40 meters/minute, Xiaohong uses 15 minutes..

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Update Time: 2024-09-04

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