Explanation:
remember, the sum of all angles in a triangle is always 180°.
1.
since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.
which makes this an isoceles triangle.
so, the second leg is 6 too.
the baseline (Hypotenuse) is then per Pythagoras
baseline² = 6² + 6² = 36 + 36 = 72 or 2×36
baseline = sqrt(72) = 6×sqrt(2)
2.
this is then a 30-60-90 triangle.
the left leg (a) is then 2a/2 = 10/2 = 5.
and the bottom leg is 5×sqrt(3).
3.
isoceles triangle.
so, left and right legs (a) are both 3 (from the 3×sqrt(2)).
4.
30-60-90 triangle
upper leg is then 6×sqrt(3).
the baseline is 2 times the left leg : 2×6 = 12
5.
isoceles triangle
both legs are 2 (from the 2×sqrt(2)).
6.
30-60-90 triangle
left leg is 4 (from the 4×sqrt(3)).
the baseline is 2×4 = 8.
7.
isoceles triangle.
6 = a×sqrt(2)
a (both legs) = 6/sqrt(2)
8.
30-60-90 triangle
9 = a×sqrt(3)
a (left leg) = 9/sqrt(3)
baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)
9.
due to the equal leg angles this is an isoceles triangle.
4 = a×sqrt(2)
a (both legs) = 4/sqrt(2)
10.
30-60-90 triangle
the bottom leg (a) = 2a/2 = 6/2 = 3
the left leg is then 3×sqrt(3)
11.
isoceles triangle
left leg is also 5.
baseline is 5×sqrt(2)
12.
30-60-90 triangle
12 = a×sqrt(3)
a (left leg) = 12/sqrt(3)
the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)