"Angle of Circle" PPT courseware

Description

"Angle of Circle" PPT courseware

Learning objectives of this section:

1. Understand the circumferential angle theorem, central angle theorem and two corollaries;

2. Be able to use the circumferential angle theorem, the central angle theorem and two corollaries to calculate and prove.

test you?

What is a circle angle? What about the central angle?

An angle whose vertex is on a circle and where both sides intersect the circle is called a circumferential angle.

The angle whose vertex is at the center of the circle is called the central angle.

Think about it?

As shown in the figure, observe the circumferential angle ∠ACB and the central angle ∠AOB. What is the relationship between their sizes?

∠ACB=1/2∠AOB

Circle Angle Theorem:

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

Fill it out

1. As shown in the figure, ∠A is the circumferential angle of ⊙O, ∠BOC=80°, then ∠A=_____,

2. As shown in the figure, if ∠E=46°, then ∠DOC=_____, ∠OCD=______.

Corollary 1 of the circle angle theorem:

The measure of an angle in a circle is equal to half the measure of the arc it subtends.

Corollary 2 of the circle angle theorem:

The circumferential angles subtended by the same arc or equal arcs are ______; the arcs subtended by equal circumferential angles in the same circle or congruent circles are also ______.

Corollary 3 of the circle angle theorem:

The circumferential angle subtended by a semicircle (or diameter) is ______, and the chord subtended by a 90° circumferential angle is ______.

Class exercises

1. (2008 Dongguan Research Article and Science) As shown in the figure, the projection of a point C on the circle O on the diameter AB is D, CD=4, BD=8, then the radius of the circle O is equal to _______.

Analysis: From the projection theorem, we get

2. As shown in the figure, the diameter AB of ⊙O is 10cm, the chord AC is 6cm, the bisector of ∠ACB intersects ⊙O at D, find the lengths of BC, AD and BD.

3. As shown in the figure, BC is the diameter of ⊙O, AD⊥BC, the vertical foot is D, AB=AF, BF and AD intersect at E, verify: AE=BE.

Keywords: Circumference and angle teaching courseware, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, circumference and angle PPT courseware download, .PPT format;

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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