"Exploring the Pythagorean Theorem" PPT download of the Pythagorean Theorem

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"Exploring the Pythagorean Theorem" PPT download of the Pythagorean Theorem

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Pythagorean theorem (the relationship between the three sides of a right triangle)

1. If the lengths of the two right-angled sides of a right triangle are a and b respectively, and the length of the hypotenuse is c, then which of the following relational expressions about a, b, c is incorrect (C)

A.b2=c2-a2 B.a2=c2-b2

C.b2=a2-c2 D.c2=a2+b2

2. The lengths of the two sides of a right triangle are 3 and 4 respectively, then the length of the hypotenuse is 4 or 5, and the height of the hypotenuse is (3√7)/4 or 12/5.

Knowledge Point 2: Verification of the Pythagorean Theorem

3. Among the following figures, the one that cannot verify the Pythagorean Theorem is (C)

4. A historical proof of the Pythagorean theorem uses the following figure, in which the two sides AE and EB of two congruent right triangles are on a straight line. The area equality relationship used in the proof is (D)

A.S△EDA=S△CEB

B.S△EDA+S△CEB=S△CDE

C.S quadrilateral CDAE=S quadrilateral CDEB

D.S△EDA+S△CDE+S△CEB=S quadrilateral ABCD

Knowledge point 3: Practical application of the Pythagorean theorem

5. A and B started from the same place at the same time. A walked 48 meters in the direction of 45° north by east, and B walked 36 meters in the direction of 45° south by east. At this time, they were 60 meters apart.

6. The mathematics interest group wanted to measure the height of the flagpole. The students found that the rope tied to the top of the flagpole hung down to the ground and had an extra section (as shown in Figure 1). Clever Xiaohong discovered: first measure the length m of the rope hanging down to the ground. Then straighten the rope (as shown in Figure 2), and measure the distance from the end of the rope C to the bottom of the flagpole B as n. Using the knowledge you have learned, you can find the length of the flagpole. If m=2 m, n=8 m, find the length of the flagpole. The length of AB.

Exploring the Pythagorean Theorem PPT, Part 2: Improving Comprehensive Ability

7. As shown in the figure, in △ABC, CE bisects ∠ACB, CF bisects ∠ACD, and EF∥BC. If EF=6, then the value of CE2+CF2 is (D)

A.6 B.9 C.18 D.36

8. In Rt△ABC, ∠C=90°, the perimeter is 60, and the ratio of the length of the hypotenuse to the length of a right-angled side is 13:5, then the lengths of the three sides of this triangle are (D)

A.25,23,12 B.13,12,5

C.10,8,6 D.26,24,10

9. As shown in the figure, if the small squares are all squares with side length 1, then the height of side BC in △ABC is (B)

A.1.6 B.1.4 C.1.5 D.2

Exploring the Pythagorean Theorem PPT, the third part: Expanding exploration and breakthroughs

17. The two local product purchasing stations A and B (considered as straight lines) are 25 km apart, C and D are two villages (considered as two points), DA⊥AB is at point A, and CB⊥AB is at point B. It is known DA=15 km, CB=10 km. Now we need to build another local product purchasing station E (E and AB are on the same straight line), so that the distance from villages C and D to station E is equal, then station E should be built How far is it from station A?

Solution: Because the distances from villages C and D to station E are equal, CE=DE.

In Rt△DAE and Rt△CBE, because DE2=AD2+AE2 and CE2=BE2+BC2, so AD2+AE2=BE2+BC2.

Assume AE is x km, then BE=(25-x)km,

Substituting BC=10 km and DA=15 km, we get x2+152=(25-x)2+102. The solution is x=10,

Therefore, acquisition station E should be built 10 km away from station A.

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Update Time: 2024-09-07

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