"Application of the Pythagorean Theorem" PPT Courseware 2 of the Pythagorean Theorem

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"Application of the Pythagorean Theorem" PPT Courseware 2 of the Pythagorean Theorem

review:

(1) Contents of the Pythagorean Theorem:

(2) Application of the Pythagorean Theorem:

① Find the third side if two sides are known;

② Given one side and an acute angle (special angles of 30°, 60°, 45°), find the length of the remaining sides;

③If the quantitative relationship between one side and the other two sides is known, use equations.

Variation training: In △ABC, AB=10, AC=17, the high line AD=8 on the side of BC, find the length of line segment BC and the area of ​​△ABC.

When no figure is given in the question, you should consider whether the shape of the figure is certain. If you are not sure, you need to classify and discuss it.

Variation practice: As shown in the figure, in the rectangular coordinate system, the vertex A of △ABC is (0, 6), B is (8, 0), AD bisects ∠BAC and intersects the x-axis at point D, DE⊥AB at E.

(1) Find the area of ​​△ABD;

(2) Find the coordinates of point E.

Additional exercises:

1. In △ABC, AD is the height of the side BC. If AB=l0, AD=8, AC=17, find the area of ​​△ABC.

Example 5 (1) It is known that the lengths of the two sides of a right triangle are 3 and 4 respectively, then the length of the third side is ________.

(2) In triangle ABC, AB=10, AC=17, the altitude line AD on side BC=8, find BC

Classification ideas

1. In a right triangle, if the length of two sides is known, when finding the third side, it should be classified and discussed.

2. When no figure is given in the known conditions, you should read the sentence carefully and draw the figure to avoid missing another situation.

Example 7 (2) As shown in the figure, there is a piece of right-angled triangle paper with two right-angled sides AC=6cm and BC=8cm. Now fold the right-angled side AC along the straight line AD so that it falls on the hypotenuse AB and coincides with AE. Find the length of CD.

Equation idea: In a right triangle, if the right angle side, as well as the equivalence relationship between the other right angle side and the hypotenuse are known, an equation can be established to solve it.

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"Application of the Pythagorean Theorem" PPT courseware on the Pythagorean Theorem:

"Application of the Pythagorean Theorem" Pythagorean Theorem PPT courseware classroom exercises: A true or false question. 1. If both sides of ABC are AB=5AC=12, then BC=13 ( ) 2. If ABC is a=6b=8, then c=10 ( ) Two fill-in-the-blank questions 1. In ABC, C=90 (1) If c=10a:b=3:4, then a=____b=___. (2)..

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Update Time: 2024-07-06

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