Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
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The question is incomplete below you will find the missing part.
Step 1 : Choose ONE of the following triangles complete the table below:
1. Obtuse Scalene Triangle Translation to prove SSS Congruence
or
2. Isosceles Right Triangle Reflection to prove ASA Congruence
or
3. Equilateral Equiangular Triangle Rotation to prove SAS Congruence
Original Coordinate Point
Transformation Rule
Image Coordinate Points
A (1, 4) (x,y) -> (x+ ,y -) A’ ( , )
B ( 7,4) (x,y) -> (x+ ,y - ) B’ ( , )
C (8,9) (x,y) -> (x+ ,y -) C’ ( , )
The appropriate table is also shown below.
The triangles ABC and A'B'C' are congruent by SSS through Obtuse Scalene Triangle Translation because the corresponding sides are congruent
Two triangles are congruent if their size and shape are the same.
Now we have to transform the triangle,
The coordinates of the triangle ΔABC are given as:
A = (1, 4)
B = (7,4)
C = (8,9)
so the lengths of the sides of the triangle are given by
AB= √(7-1)²+(4-4)²= √6²= 6
BC= √(8-7)²+(9-4)²= √1²+5²= √1+25= √26
CA= √(8-1)²+(9-4)²= √7²+5²= √49+25= √74
In order to prove the SSS congruence, we have to transform the triangles under the following translation rule:
(x,y) -> (x -3, y +6)
in the above translation,
The triangle will be translated 3 units left
And then translated 6 units up.
So, we have the new coordination of the points of the translated triangle ΔA'B'C'
A' = (1-3, 4+6)
A' = (-2, 10)
B' = (7-3, 4+6)
B' = (4, 10)
C' = (8-3, 9+6)
C' = (5, 15)
Now
so the lengths of the sides of the triangle are given by
A'B'= √(4-(-2))²+(10-10)²= √6²= 6
B'C'= √(5-4)²+(15-10)²= √1²+5²= √1+25= √26
C'A'= √(-2-5)²+(10-15)²= √(-7)²+(-5)²= √49+25= √74
By comparing two triangles ΔABC and ΔA'B'C'
AB ≅ A'B'
BC ≅ B'C'
CA ≅ C'A'
Hence ΔABC ≅ A'B'C' (By S-S-S rule)
By the above transformation, the triangles ABC and A'B'C' are congruent by SSS because the corresponding sides are congruent as all the points are gone through the same transformation.
Learn more about the transformation
here: brainly.com/question/4289712
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