A test on central symmetry in math is always essential for students in the fifth grade. Indeed, it is a chapter that allows them to develop new skills. Moreover, central symmetry in math requires a good command and concentration.
Exercise 1: (2.5 pts)
Leaving the construction lines visible
– S’ symmetric of S with respect to T
– T’ symmetric of T with respect to U
– U’ symmetrical of U with respect to V
– V’ symmetrical of V with respect to W
– W’ with respect to S symmetrical to W
Exercise 2: (3 pts)
Without the help of any figure
complete the following sentences(central symmetry):
è M’ is the symmetrical of M with respect to O means that the point …. is ………… of the segment […. ….].
è C is the symmetrical of B with respect to A means that the point …. is ………….. of the segment [….].
Exercise 3 : (6 pts) ‘central symmetry maths’.
1. Leaving the construction lines visible, construct the symmetrical of the figure with respect to I :
2. Name 2 parallel lines (to be justified).
3. Name 2 segments of the same length (to be justified).
Exercise 4 : (8,5 pts) ‘central symmetry maths ‘
1. Construct a triangle ABD such that: AB = BD = 4 cm and = 90°.
Construct the circle C with diameter [AB] and center C.
2. Construct the points P, J and L symmetrical to points B, C and A with respect to D.
3. Draw the symmetry of circle C with respect to point D. What is its center? What is its radius?
4. How long is the segment [PL]? Justify the answer with a property of the course.
5. Why is the line (PJ) perpendicular to the line (BD)? Justify the answer with a property of the course.
What is the symmetric of point B with respect to D?
What is the symmetry of point L with respect to D?
What can be deduced for the lines (BL) and (PA)? Justify the answer with a property of the course.
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