"Understanding Triangles" Triangle PPT Courseware (Lesson 4)

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"Understanding Triangles" Triangle PPT Courseware (Lesson 4)

Part One: Answering questions

1. How many heights does the triangle have? Can they be obtained by origami?

2. What is the positional relationship between the three straight lines of the triangle?

The intersection point of the altitude of an acute triangle is inside the angular triangle, the intersection point of the right triangle is the vertex of the right angle, and the straight line where the altitude of an obtuse triangle is located is outside the triangle compared to a point.

Understanding Triangles PPT, Part 2: Learning Objectives

1. Understand the concept, drawing method and properties of the height of a triangle, and be able to draw them in a specific triangle.

2. Explore the process of the three altitude lines of a triangle intersecting at one point and the application of altitude lines.

Understanding Triangle PPT, Part 3: Activity Exploration

Exploration Point 1: Height of Triangle

Draw a perpendicular from one vertex of a triangle to the straight line opposite its opposite side,

The line segment between the vertex and the vertical foot is called the altitude of the triangle.

Referred to as the height of the triangle.

As shown in the figure, line segment AD is the height of side BC.

Draw an acute angle △ABC at will, please draw the height of the side BC.

Draw an obtuse triangle on the paper.

Can you fold the three heights of an obtuse triangle?

In order to easily fold out the height on the side of BC, CB needs to be extended.

In order to easily fold out the height on the edge of AB, AB needs to be extended.

Can you draw the three heights of an obtuse triangle?

Is the height of side BC inside or outside the triangle?

What about the height beside AB?

Exploration point 2: Compare the height, midline and angle bisectors of triangles

Important segments of a triangle

altitude line of triangle

midline of triangle

angle bisector of triangle

Relevant conclusions

Each triangle has three altitudes, midlines, and angle bisectors, and their straight lines intersect at one point respectively. Among them, the intersection of the midline and the angle bisector of any triangle is within the triangle, while the intersection of the altitudes of an acute triangle is at the angle. Inside the triangle, the intersection point of the right triangle is the right vertex, and the straight line where the height of the obtuse triangle is located is outside the triangle compared to a point.

Understanding Triangle PPT, Part 4: In-class Testing

1. The intersection point of the three heights of a triangle happens to be a vertex of the triangle, then the triangle is ( )

A. Acute triangle B. right triangle

C. Obtuse triangle D. It's possible

2. Which of the following statements is wrong ( )

A. The three angle bisectors of a triangle intersect at one point

B. The three midlines of a triangle intersect at one point

C. The three altitudes of a triangle intersect at one point

D. The three height lines of a triangle intersect at one point

3． A line segment that can divide a triangle into two triangles of equal area is ()

A. midline b. Angle bisector C． High line D. angle bisector of triangle

Understanding Triangle PPT, Part 5: Personalized Assignment

1. As shown in the figure, AD⊥BC is at point D, GC⊥BC is at point C, CF⊥AB is at point F. Which of the following statements about height is wrong ( )

A. In △ABC, AD is the height next to BC

B. In △GBC, CF is the height next to BG

C. In △ABC, GC is the high A next to BC

D. In △GBC, GC is the height next to BC

2. As shown in the figure, CD⊥AB, the vertical foot is D, AC⊥BC, the vertical foot is C; the length of the line segment in the figure can represent the distance from the point to the straight line (or line segment) ( )

A. 1 item B. 3 items C． 5 items D. 7 items

3. As shown in the figure, it is known that in △ABC, AD is the height of the side BC, point E is on the line segment BD, and AE bisects ∠BAC. If ∠B=40°, ∠C=78°, then ∠EAD=________ °.

4. As shown in the figure, AD and CE are the two heights of △ABC. It is known that AD=10, CE=9, AB=12.

(1) Find the area of ​​△ABC;

(2) Find the length of BC.

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For more information about the "Triangles and Understanding Triangles" PPT courseware, please click on the "Triangles PPT and Understanding Triangles" PPT tag.

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Update Time: 2024-07-08

This template belongs to Mathematics courseware Beijing Normal University Edition Seventh Grade Mathematics Volume 2 industry PPT template

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