Similarity
Congruence
2D Trigonometry
3D Trigonometry (double points!)
100
When are two shapes similar?
When one is an enlargement of the other.
100
What are Congruent Triangles?
Triangles that have exactly the same size and shape
100
How do you work out the area of a triangle?
1/2a xx b xx sin(C)
100
What is a plane... in Maths
A plane is a flat surface.
200
What can you say about corresponding sides and angles of two similar shapes? (DAILY DOUBLE)
Corresponding angles are the same
Corresponding sides are in the same ratio
200
SSS (All three sides are equal) is one of the 4 methods of proving two triangles are congruent. What are the other 3?
SAS (Two sides and the included angle are equal)
AAS (Two angles and a corresponding side are equal)
RHS (Right angle, Hypotenuse and one other side are equal)
200
What is the Sine Rule?
a/(sin(A)) = b/(sin(B)) = c/(sin(C))
200
Work out the length of the diagonal AG
AE = 8cm
EG = sqrt(9^2 +12^2) = 15cm
AG = sqrt(8^2 +15^2) = 17cm
300
Are these two triangles similar? Why, or why not?
Yes, angles are all the same.
300
Are these two triangles congruent? How do you know?
Yes, AAS
300
What is the Cosine Rule (DAILY DOUBLE)
a2 = b2 + c2 -2bcos(A)
300
Work out the angle
theta
AE = 8cm
EG = sqrt(9^2 +12^2) = 15cm
theta = tan^-1(8/15)=28.1
400
These triangles are all similar. Find the lengths of a and b.
a = 4cm
b = 20cm
400
Give a reason for each pair of triangles being congruent:
Yellow: SSS
Blue: RHS
Pink: AAS
400
How would you find the length x?
x = sin(48) xx 16/sin(70)
x = 12.7cm
400
Work out the angle that the diagonal AC makes with the plane CDEF.
EC = sqrt(8^2 +12^2)=14.422..cm
theta = tan^-1(5/14.422)=19.1
500
Triangles PQR and PST are similar. Find x
x = 20cm
500
James and John both draw a triangle with one side with a length of 10cm, one angle of 45 degrees and another angle of 85 degrees.
Are these triangles congruent? Why, or why not?
No, the angles or sides drawn by James may not be corresponding to the ones drawn by John
500
How would you find the length x
x^2 = 6^2 + 7^2 - 2 xx6xx7xxcos(58)=40.486..
x = sqrt(40.486) = 6.36cm
500
AM is perpendicular to the plane BCDE. A point, P is the midpoint of the line BC. Work out the length of AM.
CE = sqrt(16^2 +16^2) = 22.6cm
CM = (CE)/2 = 11.3cm
AM = sqrt(24^2 - 11.3^2) = 21.2cm