"Opposite Angle" PPT Courseware 2

Description

"Opposite Angle" PPT Courseware 2

learning target:

1. Understand the concept of vertex angle and be able to identify it in graphics;

2. Master the property that vertex angles are equal and be able to use the properties of vertex angles to perform related reasoning and calculations.

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1. If ∠1+ ∠2= 180°, then ∠1 and ∠2 _____.

2. It is known that ∠ 1=30 °, ∠2 is the adjacent supplementary angle of ∠1, then ∠ 2=_______.

3. As shown in the figure, BP is the angle bisector of ∠ABC, ∠ABC=40 °, then ∠ABP=_______.

4. ∠1 and ∠2 are supplementary angles to each other, and ∠3 and ∠2 are also supplementary angles to each other, then ∠ 1______ ∠ 3.

1. Independent learning (read textbook P16 and P17 and complete the following questions)

Definition of vertex angle:

(1) Point out the edges and vertices of ∠1.

(2) Extend AO and DO to obtain OC and OB, forming ∠2. Observe these two angles. What are their characteristics?

(3) Summary:

Definition of vertex angle: _______________.

So we can get in the above figure: ∠ ___ and ∠___ are opposite vertex angles, and ∠___ and ∠___ are opposite vertex angles.

2. Cooperation and exchange (opposite angles are equal)

1. Operation: Each student draws a pair of opposite vertex angles and measures their degrees respectively.

Guess: In the picture below, ∠ 1= ∠ 2, ∠3= ∠4. (Why?)

Conclusion: If two angles are opposite vertex angles, then the two angles _____. Simply put: _____ is equal.

2. As shown in the figure, straight lines AB and CD intersect at point O, and ray OE is the angular bisector of ∠BOD. It is known that ∠AOD=110 °,

Find the degrees of ∠COB, ∠BOE and ∠EOD.

2. Definition of vertex angle

As shown in the figure, straight lines AB and CD intersect at point O. We call ∠1 and ∠2 the opposite vertex angles.

Characteristics of the opposite vertex angle: (Characteristics of the position of the angle)

(1) The vertices are the same;

(2) The sides of the angle are opposite extensions of each other.

3. Independent exploration:

As shown in the figure, what is the relationship between ∠1 and ∠3?

This reasoning process can be written as:

∵ ∠1+∠2=180 °, ∠3+∠2=180 ° (square angle definition)

∴ ∠ 1= ∠3 (supplementary angles of the same angle are equal)

Vertical angles are equal

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For more information about the PPT courseware "Diagonal Diagonal", please click the Diagonal Diagonal ppt tab.

"Opposite Angle" PPT courseware 3:

"Opposite Vertex Angle" PPT Courseware 3 Experiment and Investigation 1 Among the four angles obtained by the intersection of two straight lines, what are the characteristics of each two angles at the vertex and side? Exercise 1 Are 1 and 2 in the picture below opposite corners? Why? Exercise 2 As shown in the figure, straight lines AE and BD intersect at point O, ..

"Opposite Angle" PPT courseware:

"Opposite Vertical Angle" PPT Courseware Learning Objectives 1. Understand the concept of antipodal angle and be able to identify antipodal angles in graphics. 2. Be able to reason out the properties of equality of vertex angles. 3. Be able to reason and calculate using the property that vertex angles are equal. Observation and thinking 1. Read page 15 of the textbook...

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Update Time: 2024-09-06

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

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