Geometry 6. Level 1. Parts of a circle. Why is this triangle isosceles?. Two sides are radii. Find the value of x. 35. x. Find the value of x. x. 60. Find the value of x. x. Find the value of x. x. 20. Reminder: Exterior angle equals the sum of the opposite interior angles. - PowerPoint PPT Presentation
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Geometry 6
Level 1
Parts of a circle
Why is this triangle isosceles?
Two sides are radii
Find the value of x
35 x
Find the value of x
60
x
Find the value of x
x
Find the value of x
x20
Reminder: Exterior angle equals the sum of the opposite interior angles.
Find the value of x.
70 50
x
Let’s investigate
We now have two isosceles triangles
In each case their base angles are equal.
The exterior angle is twice the opposite internal angle
The exterior angle is twice the opposite internal angle
The angle at the centre is twice the angle at the circumference
at centre
2x
x
Find the value of x
x
50
Find the value of x
x
160
Find the value of x
x
90
Find the value of x
x
60
Another way of looking at this.
2x
x
Find the value of x.
240
x
Find the value of x.
110
x
Find the value of x.
135
x
Notice if AC is a diameter
2x
x
x
Find the value of x.
55x
Find the value of x.
80
x
Find the value of x.
140
x
Find the value of x.
50
x
Find the value of x.
74
x 62
Find the value of x.
74x
62
Find the value of x
x75
Find the value of y
y
75 75
Find the value of z
z
75 7575
Angles on the same arc are the same.
Angles on the same arc are the same.
Angles same arc
Why is it important?
Find A, B and C
If BC is a diameter…
x
x
2x
If BC is a diameter…
x
x
2x
y y
2y
If BC is a diameter…
x
x
2x
y y
2y
If BC is a diameter…
x
x
2x
y y
2y
in a semi-circle
If AC is a diameter, find the value of x.
50 x
If AC is a diameter, find the value of x.
50
x
If AC is a diameter, find the value of x
40
x
2x
x
360 - 2x
180 - x
x
180 - x
Cyclic Quadrilateral
• Opposite angles in a cyclic quadrilateral sum to 180 degrees.Web animation