"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5

Description

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5

Knowledge review

Circumferential angle: An angle whose vertex is on a circle and whose two sides intersect with the circle is called a circumferential angle.

Circle Angle Theorem

The circumferential angle subtended by an arc is equal to half of the central angle subtended by it.

life practice

When a player shoots at B, D, and E, his position forms three opening angles to goal AC: ∠ABC, ∠ADC, and ∠AEC. What is the relationship between the sizes of these three angles?

New knowledge exploration

As shown in Figure 1, an arc AC in a circle faces many circumferential angles. What is the relationship between the sizes of these angles? Why?

As shown in Figure 2, AB=EF in the circle, then what is the relationship between the sizes of ∠C and ∠G? Why?

Corollary to the circle angle theorem

In the same circle or equal circles, the circumferential angles subtended by the same arc or equal arcs are equal; the arcs subtended by equal circumferential angles are also equal.

Problem discussion

1. As shown in Figure (1), BC is the diameter of ⊙O, and A is any point on ⊙O. Can you determine the degree of ∠BAC?

2. As shown in Figure (2), the circumferential angle ∠BAC =90º, does the chord BC pass through the center O? Why?

Corollary 2 of the circle angle theorem

The circumferential angle subtended by a semicircle (or diameter) is a right angle; the chord subtended by a 90° circumferential angle is the diameter.

Class exercises

1.Judgement questions:

(1) The circumferential angles subtended by equal arcs are equal. ( )

(2) The arcs subtended by equal circumferential angles are also equal. ( )

(3) The chord subtended by an angle of 90° is the diameter. ( )

(4) The circumferential angles subtended by the same chord are equal. ( )

2. Fill in the blanks:

(1) As shown in the figure, ∠BAC=____, ∠DAC=____.

(2) As shown in the figure, the diameter of ⊙O is AB=10cm, C is a point on ⊙O, ∠BAC=30°, then BC=____cm

knowledge deepening

As shown in the figure, taking the radius OA of ⊙O as the diameter, draw ⊙O1, and the chord AD of ⊙O intersects ⊙O1 at C, then

(1)The positional relationship between OC and AD is___________;

(2)The positional relationship between OC and BD is___________;

(3) If OC = 2cm, then BD = ______cm.

Class summary

1. What knowledge did we learn in this lesson?

Two Corollaries of the Circle Angle Theorem

2. What methods have we learned in this lesson?

How to draw auxiliary lines:

(1) Construct the circumferential angle on the diameter.

(2) Construct the circumferential angle subtended by the same arc.

Thinking questions

It is known that the isosceles triangle ABC with vertex angle ∠A=50° is inscribed in O, and D is a point above O, then the degree of ∠ADB is ( )

A.50° B.65° C.50° or 65° D.65° or 115°

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"The Relationship between the Circumferential Angle and the Central Angle" Circle PPT Courseware 4:

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 4 Circumferential Angle Definition: An angle whose vertex is on a circle and both sides intersect with the circle is called a circumferential angle. Features: ① The vertex of the angle is on the circle. ② Both sides of the angle intersect with the circle Intersect. Hands on the relationship between the circumferential angle and the central angle of the circle subtended by the same arc..

"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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Update Time: 2024-09-08

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

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