"Understanding Triangles" Triangle PPT Courseware 7

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"Understanding Triangles" Triangle PPT Courseware 7

The three heights of an acute triangle

Do it

Each person prepares an acute-angled triangle piece of paper.

(1) Can you draw the three heights of this triangle?

(2) Can you get them by origami?

(3) What is the positional relationship between these three heights?

Communicate your results with peers.

Are the three heights of an acute triangle inside or outside the triangle?

Three heights of a right triangle

Do it

Draw a right triangle on the paper.

(1) Draw the three heights of a right triangle. What is their positional relationship?

Communicate your results with peers.

The three altitudes of a right triangle intersect at the vertex of the right angle.

The three heights of an obtuse triangle

Do the three altitudes of an obtuse triangle intersect at one point?

The three heights of an obtuse triangle do not intersect at one point

The three height lines of an obtuse triangle intersect at one point

Definition of angle bisector of a triangle

The "angle bisector" we learned before is a ray,

Is "angle bisector of a triangle" still a ray?

In a triangle, the bisector of an interior angle intersects its opposite side. The line segment between the vertex of the angle and the intersection point is called the angle bisector of the triangle.

Properties of angle bisectors of triangles

(1) Can you draw the three angle bisectors of a triangle?

(2) Can you get them by origami?

(3) In each triangle, what is the positional relationship between the three angle bisectors?

Communicate your results with peers.

The "midline" of a triangle

In a triangle, the line segment connecting a vertex to the midpoint of the opposite side is called the median of the triangle.

Discuss

(1) Draw an acute triangle on paper and draw its three midlines.

What is their positional relationship? Communicate with your companions.

(2) Do the three midlines of an obtuse triangle and a right triangle have the same positional relationship?

Fold it, draw it, and communicate with your peers·

Expansion exercises

1. Among the following sets of figures, in which set of figures AD is the height of △ABC ( )

2. If the intersection point of the three heights of a triangle is exactly a vertex of the triangle, then the triangle is ( )

A. Acute triangle B. Right triangle

C. Obtuse triangle D. Acute triangle

3. The three heights of the triangle intersect at one point, and this point is determined at ( )

A. The inside of the triangle B. The outside of the triangle

C. On one side of the triangle D. Uncertain

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Update Time: 2024-07-29

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