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Category | Format | Size |
---|---|---|
Beijing Normal University Ninth Grade Mathematics Volume 2 | pptx | 6 MB |
Description
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 4
Definition of circumferential angle: An angle whose vertex is on a circle and both sides intersect the circle is called a circumferential angle.
Characteristics: ① The vertex of the angle is on the circle. ② Both sides of the angle intersect the circle.
The relationship between the circumferential angle and the central angle of a circle subtended by the same arc
Hands-on operation: In the same circle, draw the circumferential angle (∠ACB) and the central angle (∠AOB) of the same arc, and measure the sizes of the circumferential angle and central angle you drew.
Note: The position of the center and the angle of the circle
basic training
1. Which of the following propositions is true ( )
(A) The angle of the vertex on the circumference is called the circumferential angle
(B) The arc subtended by a 60º circumferential angle is 30º
(C) The circumferential angle subtended by an arc is equal to the central angle subtended by it
(D) The angle subtended by an arc of 120º is 60º
2. As shown in the figure on the right, in ⊙O, ∠ACB = 130º, then ∠AOB=______.
3. Find the measure of ∠α in the circle.
4. As shown in the figure, OA⊥BC, ∠AOB=50°, then ∠CDA=25°
5. In a circle with radius R, the circumferential angle subtended by a chord of length R is 30° or 150°
Class summary
1. What new knowledge did you learn in this lesson?
2. What knowledge did you apply?
3. What methods were used to solve problems during the learning process?
Improve ability
1. As shown in the figure, OA, OB, and OC are all radii of ⊙0, ∠AOB=2∠BOC
What is the relationship between the size of ∠ACB and ∠BAC? Why?
2. As shown in the figure, points A, B, C, D, and E are all on ⊙0, then what degree is ∠A+∠B+∠C+∠D+∠E equal to? Why?
Analysis: The sum of the arcs subtended by the five circumferential angles ∠A∠B∠C∠D∠E is exactly a circle, and the central angle subtended by a circle is 360°.
So: ∠A+∠B+∠C+∠D+∠E=180°
3. As shown in the figure, in ⊙O, BC=2DE, ∠BOC=84°, find the degree of ∠A.
Keywords: circle teaching courseware, teaching courseware on the relationship between the circumferential angle and the central angle of a circle, Beijing Normal University edition ninth grade mathematics volume 2 PPT courseware, ninth grade mathematics slide courseware download, circle PPT courseware download, relationship between the circumferential angle and the central angle PPT Courseware download, .ppt format
For more information about the "Relationship between Circumferential Angle and Central Angle of a Circle" PPT courseware, please click on the "Relationship between Circumferential Angle and Central Angle of a Circle" ppt tag.
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5:
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5 Knowledge Review Circumferential Angle: The vertex is on the circle, and its two sides have another intersection with the circle. An angle like this is called a circumferential angle. Circumferential Angle Theorem The circumference of a circle subtended by an arc An angle is equal to half of the central angle of the circle it subtends. Health...
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 3:
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 3 Knowledge Review 1. A circle is an axially symmetrical figure. The symmetry axis of a circle is any straight line passing through the center of the circle. It has countless symmetry axes. 2. A circle is also a centrally symmetrical figure. It The center of symmetry is the center of the circle. 3. The vertex is at the center of the circle..
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 2:
"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 2 1. Review 1. What is a circumferential angle? The vertex is on the circle and the angle where the two sides intersect the circle is called the circumferential angle. 2. Fill in the blanks: ⑴The _______ subtended by an arc is equal to half of the degree _________ subtended by it. ⑵Circumference..
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