"Angle bisectors, midlines and heights of triangles" PPT

Description

"Angle bisectors, midlines and heights of triangles" PPT

Part One: Review of Related Knowledge

1. Definition of vertical 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 2 content: Height of triangles

Draw a perpendicular from one vertex of a triangle to the straight line where its opposite side lies, and the line segment between the vertex and the vertical foot

It is called the height of this side of the triangle, or simply 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.

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 3 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 this side of the triangle.

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

∵AD is the angle bisector of △ABC

∴∠ BAD = ∠ CAD =1/2∠BAC

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 4: 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 D.The opposite side of ∠C is DE

3. As shown in the figure, in ΔABC, AE is the center line, AD is the angle bisector, and AF is the height. fill in the blank:

(1)BE=_____=_____;

(2)∠BAD=_____= _____;

(3) ∠AFB=_____ =90°;

Angle bisectors, midlines and heights of triangles PPT, Part 5: Knowledge summary

What did we learn today?

1. Relevant concepts such as the altitude, midline, and angle bisector of a triangle and how to draw them.

2. Geometric expressions and simple applications of the altitude, midline and angle bisector of a triangle.

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 "Angle Bisectors of Triangles Median and Height" PPT courseware, please click the Angle Bisectors of Triangles Median and Height ppt label.

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

"Angle bisectors, midlines and heights of triangles" PPT download Part 1 content: Teaching objectives 1. Understand relevant concepts such as heights, midlines and angle bisectors of triangles. 2. Master the drawing of heights, midlines and angle bisectors of any triangle Method, recognize triangles through observation..

"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..

File Info

Update Time: 2024-10-19

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

Preview