Geometry construction - practice problems - page 5 of 10
Number of problems found: 189
- Point distance marking
In the plane, the points A, B, and C are given 3 cm apart, and they do not lie in the same straight line. Mark the set of all points whose distance from all three points is less than or equal to 2.5 cm. - Equilateral triangle circle
There is a circle with a radius of 2.5 cm and point A, which lies on it. Write an equilateral triangle ABC in the circle. - Square diagonal construction
There are three different points, C, E, and F, in the plane. Please draw the square ABCD when E and F lie on the diagonals of this square. How many solutions does the task have? - Rectangular trapezoid ZIMA
I have a rectangular trapezoid ZIMA (the right angle at the top of Z. ZIMA = winter in English) ZI-7 cm, ZM-5 cm, AM-3.5 cm, and we have to write the procedure to construct this trapezoid. - Triangle circle construction
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - Square central symmetry
Draw a square KLMN, a point R that is a point of the square, and a point S that is not a point of this square. Draw the image of the square KLMN in central symmetry with the center : a) at point s b) at point M c) at point R - Geometric drawing exercise
Draw in one picture: a) straight line RZ b) YZ for which YZ is perpendicular to RZ c) the half-line RS diverging with YZ and with the line RZ d) point F, which lies on YZ outside the already selected points e) point H, which lies on the half-line RS and t - Draw triangle
Construct an isosceles triangle ABC, if AB = 7 cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm. - Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. ) - Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8 cm, inscribed circle radius r = 1.5 cm - Parallels and one secant
There are two different parallel lines, a, b, and line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - Construct rhombus - MO
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all possibilities. How long is a side of a rhombus? - Calculate sides
In the triangle, the side length AB = 6 cm, the height to side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Circle line tangent
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Circle position sketch
Sketch the relative position of the circles k1 (S1, r1 = 5 cm) and k2 (S2, r2 = 3 cm) and k / S1S2 / = 0 cm and give its name. - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Family 5 The Plavecký family built a pool which is 120 cm deep. a/The bottom of the pool has a thickness of 10 cm, the side walls 20 cm. The pool has the shape of a cuboid with a base of 3 m x 5 m. How many cubic metres did they use for its construction? b/Their s
- Dividing a Circle
Draw a circle k, r = 4 cm, and divide it into two parts in a ratio of 1:5. - Rectangle drawing calculation
Draw rectangles. Color them and calculate the circuits and areas. KLMN: KL = 5CM LM = 3CM rectangle OPQR OP = 4 cm PQ = 3.5 cm - Square drawing calculation
Draw squares. Color them and calculate the perimeter and areas square ABCD a = 3 cm square EFGH b = 4 cm
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