"Triangle" PPT courseware 4

"Triangle" PPT courseware 4

midline of triangle

(1) Connect the vertex A of △ABC to the midpoint D of the side BC it faces, and the resulting line segment AD is called the midline on the side BC of △ABC.

(2) Properties of the midline of a triangle:

①As shown in the figure above, AD is the center line of △ABC, then (BD)=(DC)=1/2BC;

②The area of ​​△ABD = (the area of ​​△ADC or half the area of ​​△ABC)

Explore and discover

When a classmate drew the midline of a triangle, the midlines of both sides intersected at point G, and found that the midline of the third side also passed through point G. Is this true for all the midlines of the three sides of a triangle? Can you please give it a try?

angle bisector of triangle

Draw the bisector AD of ∠A and intersect the side BC opposite to ∠A at point D. The resulting line segment AD is called the angle bisector of △ABC.

①AD is the angle bisector of △ABC, then there is (∠BAD)=(∠DAC)=1/2∠BAC

②Do the three angles of a triangle bisect and intersect at one point? Please draw a picture to verify.

③Conclusion: The three angle bisectors of a triangle intersect at one point

altitude line of triangle

Draw a perpendicular line from the vertex A of △ ABC to the straight line on the side BC opposite to it. The vertical foot is D. The resulting line segment AD is called the altitude line on the side BC of △ ABC.

①What are the differences between the three ∠Bs in Figures (1), (2), and (3)? Where is the height AD on side BC of these three △ABC located in their respective triangles? Can you tell the pattern?

② The three angle bisectors and the midline of a triangle all intersect at one point. Some students guessed that the straight line where the three altitude lines of the triangle also intersect at one point? Do you think it is right? Please give it a try.

③Conclusion: The three altitudes of a triangle intersect at one point. The two altitudes of a right triangle are right-angled sides, and the two altitudes of an obtuse triangle are outside the triangle.

Reinforcement exercises:

1.The following statement

①The altitude, midline and angle bisector of a triangle are all line segments;

②The altitude, midline, and angle bisectors of a triangle are all inside the triangle;

③The altitude, midline, and angle bisectors of the triangle all intersect at one point;

④ There is only one altitude line of a right triangle; the correct number is ( )

A.1 B.2 C.3 D.4

2. As shown in the figure, in △ABC, AB=2cm, BC=4 cm. What is the ratio of the height AD to CE of △ABC?

Solution: Known from the area formula of a triangle; AD/EC=4:2

Harvest and experience

1. Learned how to draw and represent angle bisectors, midlines, and altitudes of triangles.

2. Each triangle has three midlines, three angle bisectors, and three altitudes.

3. The three angle bisectors and three midlines of a triangle intersect at a point inside the triangle. The three altitudes of an acute triangle intersect at a point inside the triangle. The three altitudes of a right-angled triangle intersect at the vertex of the right angle of the triangle. The extensions of the three altitudes of an obtuse triangle intersect outside the triangle. a little.

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