Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "CIRCLES 2 Moody Mathematics. ANGLE PROPERTIES: Moody Mathematics Let’s review the methods for finding the arcs and the different kinds of angles found."— Presentation transcript:

1 CIRCLES 2 Moody Mathematics

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

3 Moody Mathematics The measure of a minor arc is the same as… …the measure of its central angle.

4 Example:

5 Moody Mathematics The measure of an inscribed angle is… …half the measure of its intercepted angle.

6 Example:

7 Moody Mathematics The measure of an angle formed by a tangent and secant is … …half the measure of its intercepted arc.

8 Example:

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

10 Example:

11 Moody Mathematics 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.

12 Example:

13 Moody Mathematics 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.

14 Example:

15 PROPERTIES: Complete the theorem relating the objects pictured in each frame. 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…” 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 * represents the rest of the phrase. 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.

19 In the same circle,* Congruent central angles......intercept congruent arcs.

20 In the same circle,* Congruent Chords......intercept congruent arcs.

21 Tangent segments from an exterior point to a circle…...are congruent.

22 The radius drawn to a tangent at the point of tangency…...is perpendicular to the tangent.

23 If a diameter (or radius) is perpendicular to a chord, then…...it bisects the chord… …and the arcs.

24 In the same circle,* Congruent Chords......are equidistant from the center.

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

26 Moody Mathematics If two Inscribed angles intercept the same arc......then they are congruent.

27 If an inscribed angle intercepts or is inscribed in a semicircle …...then it is a right angle.

28 If a quadrilateral is inscribed in a circle then each pair of opposite angles …...must be supplementary. (total 180 o )

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

30 Example:

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

32 Example:

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

34 Example:

35 Let’s Practice!

36 Moody Mathematics Example: Given

37 Moody Mathematics Example:

38 Moody Mathematics Example:

39 Moody Mathematics Example:

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

41 Moody Mathematics Example:

42 Moody Mathematics Example:

43 Moody Mathematics Example:

44 Moody Mathematics Example:

45 Moody Mathematics Example:

46 Moody Mathematics Example:

47 Example: Of the following quadrilaterals, which can not always be inscribed in a circle? A.Rectangle B.Rhombus C.Square D.Isosceles Trapezoid

48 Moody Mathematics Example:

49 Moody Mathematics Example:

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

51 THE END! Now go practice!


Download ppt "CIRCLES 2 Moody Mathematics. ANGLE PROPERTIES: Moody Mathematics Let’s review the methods for finding the arcs and the different kinds of angles found."

Similar presentations


Ads by Google