340 likes | 459 Views
Other Angle Relationships In Circles . Geometry Chapter 10 A BowerPoint Presentation. 2 chords. Draw 2 intersecting chords in your circle Label a pair of vertical angles as angles 1 and 2 What do you know about angles 1 and 2?. 2 chords. Draw 2 intersecting chords in your circle
E N D
Other Angle Relationships In Circles Geometry Chapter 10 A BowerPoint Presentation
2 chords • Draw 2 intersecting chords in your circle • Label a pair of vertical angles as angles 1 and 2 • What do you know about angles 1 and 2?
2 chords • Draw 2 intersecting chords in your circle • Label a pair of vertical angles as angles 1 and 2 • What do you know about angles 1 and 2? • They are congruent!
2 chords • Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent?
2 chords • Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent? • No!
2 chords • Find the measures of angles 1 & 2
2 chords • Find the measures of angles 1 & 2 Both angles = 110o
2 chords • Find x
2 chords • Find x x = 80
2 secants • Put a point outside the circle (probably to the right) • Draw two secants that go through that point and through the circle • Do you see how the angle you’ve created intercepts two arcs in the circle?
2 secants • Find the measure of angle 1
2 secants • Find the measure of angle 1 Angle 1 = 50o
2 secants • Find x
2 secants • Find x x = 130
1 secant & 1 tangent • Put a point outside the circle (probably to the right) • Draw a secant that goes through the circle and through the point • Draw a tangent that touches the circle at one point and goes through your point • Do you see how the angle you’ve created intercepts two arcs in the circle?
1 tangent & 1 secant • Find the measure of angle 1
1 tangent & 1 secant • Find the measure of angle 1 Angle 1 = 45o
1 secant & 1 tangent • Find x
1 secant & 1 tangent • Find x x = 90
2 tangents • Put a point outside the circle (probably to the right) • Draw two tangents that each touch the circle once and intersect at your point • Do you see how the angle you’ve created intercepts two arcs in the circle?
2 tangents • Find the measure of angle 1 (There is enough information!)
2 tangents • Find the measure of angle 1 (There is enough information – how big is green arc?)
2 tangents • Find the measure of angle 1 Angle 1 = 80o
2 tangents • Find x
2 tangents • Find x x– (360 – x)= 2 (50)
2 tangents • Find x x = 230