Download presentation

Presentation is loading. Please wait.

1
CIRCLES 2 Moody Mathematics

2
ANGLE PROPERTIES: Let’s review the methods for finding the arcs and the different kinds of angles found in circles. Moody Mathematics

3
**The measure of a minor arc is the same as…**

…the measure of its central angle. Moody Mathematics

4
Example: Moody Mathematics

5
**The measure of an inscribed angle is…**

…half the measure of its intercepted angle. Moody Mathematics

6
Example: Moody Mathematics

7
**The measure of an angle formed by a tangent and secant is …**

…half the measure of its intercepted arc. Moody Mathematics

8
Example: Moody Mathematics

9
**...is half the sum of the two intercepted arcs.**

The measure of one of the vertical angles formed by 2 intersecting chords ...is half the sum of the two intercepted arcs. Moody Mathematics

10
Example: Moody Mathematics

11
**…half the difference of the measures of its two intercepted arcs.**

The measure of an angle formed by 2 secants intersecting outside of a circle is… …half the difference of the measures of its two intercepted arcs. Moody Mathematics

12
Example: Moody Mathematics

13
**…half the difference of the measures of its two intercepted arcs.**

The measure of an angle formed by 2 tangents intersecting outside of a circle is… …half the difference of the measures of its two intercepted arcs. Moody Mathematics

14
Example: Moody Mathematics

15
**PROPERTIES: Complete the theorem relating the objects pictured in each frame.**

Moody Mathematics

16
**Note: Many of our theorems begin the same way, “In the same circle, or in congruent circles…”**

Moody Mathematics

17
**So: We will just start “In the same circle. …” where the**

So: We will just start “In the same circle*…” where the * represents the rest of the phrase. Moody Mathematics

18
**All radii in the same circle,* …**

...are congruent. Moody Mathematics

19
**In the same circle,* Congruent central angles...**

...intercept congruent arcs. Moody Mathematics

20
**In the same circle,* Congruent Chords...**

...intercept congruent arcs. Moody Mathematics

21
**Tangent segments from an exterior point to a circle…**

...are congruent. Moody Mathematics

22
**The radius drawn to a tangent at the point of tangency…**

...is perpendicular to the tangent. Moody Mathematics

23
**If a diameter (or radius) is perpendicular to a chord, then…**

...it bisects the chord… …and the arcs. Moody Mathematics

24
**In the same circle,* Congruent Chords...**

...are equidistant from the center. Moody Mathematics

25
**Example: Given a circle of radius 5” and two 8” chords**

Example: Given a circle of radius 5” and two 8” chords. Find their distance to the center. Moody Mathematics

26
**If two Inscribed angles intercept the same arc...**

...then they are congruent. Moody Mathematics

27
**If an inscribed angle intercepts or is inscribed in a semicircle …**

...then it is a right angle. Moody Mathematics

28
**If a quadrilateral is inscribed in a circle then each pair of opposite angles …**

...must be supplementary. (total 180o) Moody Mathematics

29
**If 2 chords intersect in a circle, the lengths of segments formed have the following relationship:**

Moody Mathematics

30
Example: Moody Mathematics

31
**If 2 secants intersect outside of a circle, their lengths are related by…**

Moody Mathematics

32
Example: Moody Mathematics

33
**If a secant and tangent intersect outside of a circle, their lengths are related by…**

Moody Mathematics

34
Example: Moody Mathematics

35
Let’s Practice!

36
Example: Given Moody Mathematics

37
Example: Moody Mathematics

38
Example: Moody Mathematics

39
Example: Moody Mathematics

40
**Example: Given a circle of radius 13” and two 24” chords**

Example: Given a circle of radius 13” and two 24” chords. Find their distance to the center. Moody Mathematics

41
Example: Moody Mathematics

42
Example: Moody Mathematics

43
Example: Moody Mathematics

44
Example: Moody Mathematics

45
Example: Moody Mathematics

46
Example: Moody Mathematics

47
**Example: Of the following quadrilaterals, which can not always be inscribed in a circle?**

Rectangle Rhombus Square Isosceles Trapezoid

48
Example: Moody Mathematics

49
Example: Moody Mathematics

50
**Example: Regular Hexagon ABCDEF is inscribed in a circle.**

Moody Mathematics

51
THE END! Now go practice!

Similar presentations

Presentation is loading. Please wait....

OK

Circles Chapter 12.

Circles Chapter 12.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sea level rise news Ppt on surface chemistry Ppt on db2 architecture overview Ppt on adr and gdr group Ppt on conservation of species Ppt on water cycle for kindergarten Ppt on nepali culture show Ppt on articles for class 7 Ppt on air pollution in hindi Ppt on tunnel diode manufacturers