Circles and Angles L4.notebook August 18, 2015 'DLO\ 3UDFWLFH 3OHDVH FRPSOHWH LQ WKH EDFN RI \RXU FODVV ZRUN MRWWHUV Q1. Solve 5(x - 1) = 3(x + 2) Q5. Round 6781000 Q2. Find 67% of 800 Q3. Q4. Rearrange the formula so t is the subject xt + 5 = b to 1 significant figure L.I: Today we will be learning about tangents to circles. S.C: I will be able to draw a tangent to a circle and recognise the relationship between radius and tangent. I will be able to use this knowledge to find missing angles in the triangles created. Angles in Triangles and Circles Key things to remember: • Equilateral triangles have • Isosceles triangles have • All the angles in a triangle add to get ___ Tangents to Circles A tangent to a circle is a straight line that touches the circle at only one point . Tangents to Circles - Investigation 1. Use your pair of compasses to draw 5 circles of various sizes. 2. Mark in the centre (origin O) on your circle. 3. Plot a point on the circle. 4. Draw a tangent at that point. 5. Draw a radius that meets the point on the circumference. 6. Measure the angle that the radius makes with the tangent. Tangents to Circles - Investigation What do we notice? ** A radius drawn to a tangent is perpendicular to the tangent (makes a 90 0 angle)
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Circles and Angles L4.notebook August 18, 2015
Daily Practice 25.5.2015Please complete in the back of your class work jotters.
Q1. Solve 5(x - 1) = 3(x + 2) Q5. Round 6781000
Q2. Find 67% of 800
Q3.
Q4. Rearrange the formula so t is the subject
xt + 5 = b
to 1 significant figure L.I: Today we will be learning about tangents to circles.
S.C: I will be able to draw a tangent to a circle and recognise the relationship between radius and tangent. I will be able to use this knowledge to find missing angles in the triangles created.
Angles in Triangles and Circles
Key things to remember:
• Equilateral triangles have
• Isosceles triangles have
• All the angles in a triangle add to get ___
Tangents to Circles
A tangent to a circle is a straight line that touches the circle at only one point.
Tangents to Circles - Investigation1. Use your pair of compasses to draw 5 circles of various sizes.
2. Mark in the centre (origin O) on your circle.
3. Plot a point on the circle.
4. Draw a tangent at that point.
5. Draw a radius that meets the point on the circumference.
6. Measure the angle that the radius makes with the tangent.
Tangents to Circles - Investigation
What do we notice?
** A radius drawn to a tangent is perpendicular to the tangent (makes a 900 angle)
Circles and Angles L4.notebook August 18, 2015
Tangents to Circles
A tangent kite is made when you have two tangents to a circle that join to make a kite.
o
Daily Practice 26.5.2015
Q1. Write each of the following as a decimal of hours
L.I: Today we will be continuing to learn about tangents to circles.
S.C: I will be able to use my knowledge of tangents to circles to find missing angles in the triangles created.
Tangents to CirclesExamples:
1. Calculate the size of x
170
Ox 0
1310
P
O
QR
2. What is the value of the angles
(i) PQO
(ii) QPR
y 0
Tangents to Circles
I am able to draw a
tangent to a circle and
recognise the relationship
between radius and tangent.
I am able to use this
knowledge to find missing
angles in the triangles created.
Success?
Circles and Angles L4.notebook August 18, 2015
Q1. Factorise 6x2 ‐ 24x
Q2. Multiply out and simplify 7(x ‐ 1) + 2(x + 3)
Q3. Calculate the distance John travels if he runs at 10mph for 45 minutes
Q4. Round 8716.5 to the nearest unit
Q5. John earns £2200 per month, he gets a pay rise of 3.5%. How much is he now earning
Daily Practice 27.5.2015
L.I: Today we will be learning how to draw a triangle in a semi-circle and investigate the angles made.
S.C: I will be successful if I can identify what type of angle is created when I draw a triangle in a semi-circle and I can use this knowledge to find other missing angles.
Triangles in semi- circles Investigation
1. Draw 5 different sized circles.
2. Draw a diameter on each.
3. Draw a triangle in each circle using the diameter as the base. The top of the triangle must touch the circumference.
4. Measure the angle at the top of the triangle.
Triangles in semi- circles Investigation
What do we notice?
http://www.mathopenref.com/semiinscribed.html
Given triangle ABC, where AC is the diameter. Angle ABC is right-angled.
A
B
C
Triangles in semi- circles Investigation
Proof:
This theorem can be proved by using two isosceles triangles.x0 y0