 # Control on central symmetry of math in 5th grade.

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
build :

– 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.

6.Complete :

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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