"Angle bisectors, midlines and heights of a triangle" PPT download

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"Angle bisectors, midlines and heights of a triangle" PPT download

Part One: Teaching Objectives

1. Understand relevant concepts such as the altitude, midline, and angle bisector of a triangle.

2. Master how to draw the height, midline and angle bisector of any triangle, and realize through observation that the three heights, three midlines and three angle bisectors of a triangle intersect at one point respectively.

3. Improve students’ hands-on operation and problem-solving abilities.

Key points and difficulties in teaching

Teaching focus: simple application of the concepts of altitude, midline and angle bisector of a triangle and their geometric language expression.

Teaching difficulty: How to draw the height of an obtuse triangle.

Angle bisectors, midlines and heights of triangles PPT, Part 2: Review of related knowledge

1. Definition of perpendicular line: When one of the four angles formed by the intersection of two straight lines is a right angle, the two straight lines are said to be perpendicular to each other, and one of the straight lines is called the perpendicular to the other straight line.

2. The definition of the midpoint of a line segment: the point that divides a line segment into two equal line segments.

3. The definition of the bisector of an angle: A ray divides an angle into two equal angles. This ray is called the bisector of the angle.

Angle bisectors, midlines and heights of triangles PPT, Part 3 content: Height of triangles

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, or simply the height of the triangle.

The three heights of an acute triangle

The three altitudes of an acute triangle intersect at the same point.

The three heights of an acute triangle are inside the triangle.

Three heights of a right triangle

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

The three heights of an obtuse triangle

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

Angle bisectors, midlines and heights of triangles PPT, Part 4 content: Midlines and angle bisectors of triangles

midline of triangle

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

The three midlines of a triangle intersect at one point, and the intersection point is inside the triangle. This intersection point is called the center of gravity of the triangle.

Draw a random triangle, and then use a ruler to draw the midline of the three sides of the triangle. What do you find?

angle bisector of triangle

In a triangle, the angle 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.

The three angle bisectors of a triangle intersect at one point, and the intersection point is inside the triangle

Draw a triangle at random, and then use a protractor to draw the angle bisectors of the three angles of the triangle. What do you find?

Angle bisectors, midlines and heights of triangles PPT, Part 5: Expansion exercises

1. As shown in Figure 1, in △ABC, ∠ACB=90°, turn △ABC 180° along the straight line AC, so that point B falls at the position of point B′, then the line segment AC has the property ( )

A. It is the midline on side BB′ B. It is the height on side BB′

C. It is the angle bisector of ∠BAB′ D. The above three properties are combined into one

2. As shown in Figure 2, D and E are the midpoints of sides AC and BC of △ABC respectively. Which of the following statements is incorrect ( )

A.DE is the midline of △BCD

B.BD is the midline of △ABC

C.AD=DC,BD=EC

3. Fill in the blanks:

(1) As shown in Figure (1), AD, BE, and CF are the three midlines of ΔABC, then AB=2____, BD=____, AE=____.

(2) As shown in Figure (2), AD, BE, and CF are the three angle bisectors of ΔABC, then ∠1=____, ∠3=____, ∠ACB=2____.

Angle bisectors, midlines and heights of triangles PPT, Part 6 content: Classroom thinking questions

As shown in the figure, in △ABC, ∠1=∠2, G is the midpoint of AD, extend BG to intersect AC at E, F is the point above AB, CF⊥AD is at H, determine which of the following statements are correct and which are incorrect of.

①AD is the angle bisector ( ) of △ ABE

②BE is the midline on side AD of △ ABD ( )

③BE is the midline ( ) on side AC of △ ABC

④CH is the height ( ) on side AD of △ ACD

The height, midline and angle bisector of a triangle are all line segments

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for seventh grade volume 2, angle bisector midline and height of a triangle PPT download, .PPT format;

For more information about the PPT courseware "Medium and Height of Angle Bisectors of Triangles", please click on the Median and Height of Angle Bisectors of Triangles PPT tab.

"Angle bisectors, midlines and heights of triangles" PPT courseware:

"Angle bisectors, medians and heights of triangles" PPT courseware Part 1: Learning objectives 1 Understand the angle bisectors, medians, heights and their properties of triangles. Able to draw angle bisectors, midlines and heights of known triangles. Let students understand that the superposition method is the opposite in geometry..

"Angle bisectors, midlines and heights of triangles" PPT:

"Angle Bisectors, Medians and Heights of Triangles" PPT Part 1 Content: Review of Related Knowledge 1. Definition of Perpendicular: When one of the four angles formed by the intersection of two straight lines is a right angle, it is said that these two angles are right angles. Straight lines are perpendicular to each other, and one of the straight lines is called the other..

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Hebei Education Edition Seventh Grade Mathematics Volume 2 industry PPT template

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