Geometry Exploration and Activities
Engage in interactive geometry activities involving circles, triangles, angles, and more to enhance understanding through hands-on learning experiences. Explore concepts of diameters, areas, angles, and quadrilaterals in a visual and collaborative setting.
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Presentation Transcript
From last week ? A circle has equation ?2+ ?2= 64 ? What is the diameter of the circle? a) 64 b) 32 c)16 d)8 ? From last month Work out the area of this triangle From last year Expand and Simplify (? + 7)(? 3)
From last week ? = 8 so d = 16 From last month 1 2 6 9 sin130 = 20.7 ??2 From last year ?2+ 4? 21
1. Using the points provided draw a diameter. 2. Make a triangle using your diameter and any point of the circumference. 3. Measure the angle opposite the centre of the circle. Discuss your angle with your partner, what do you notice?
? Proof ? ? Discuss: How do we know that these angles are equal? ? ? + ? + ? + ? = 180 2? + 2? = 180 ? + ? = 90
On your whiteboards: Work out the missing angle
On your whiteboards: Work out the missing angle
On your whiteboards: Work out the missing angles
Work out the missing angles 1. 2. 3. 5. 4.
Mark your work 1. x = 39 2. y = 48 3. z =74 4. x = 53 5. y = 33 and z = 49
Challenge The radius of this circle is 10cm. Work out the area of the quadrilateral ABDE
1. Using the points provided draw a chord. 2. Make a triangle using your chord and any point of the circumference. 3. Make another triangle using the same chord and the centre of the circle. 4. Measure the angle subtended by the arc at the centre of the circle. 5. Measure the angle subtended by the arc at the circumference. Discuss your angles with your partner, what do you notice?
B Proof A ? Discuss: ?? ? ?? How do we know that these angles are equal? O What expression can we write for angle BOC? ? ? Angle BOC = 180 2x C What expression can we write for this angle? 180 180 2x = 2x What expression can we write for this angle? 2y
B ????? ??? = ? + ? A ? ?? ? ?? O ????? ??? = 2? + 2? ? ? ????? ??? = 2(? + ?) C
The angle at the centre is double the angle at the circumference. Demo 2
On your whiteboards: Work out the missing angle
On your whiteboards: Work out the missing angle
On your whiteboards: Work out the missing angle
On your whiteboards: Work out the missing angle
Work out the missing angles 1. 2. 3. 5. 4.
Mark your work 1. x = 34 2. y = 46 3. y = 212 4. x = 29 5. y = 100
Challenge The radius of this circle is 10cm. Work out the area of the quadrilateral ABDC
