Geometry construction - high school - practice problems - page 2 of 3
Number of problems found: 46
- Block-shaped 7976
A block-shaped pool with a volume of 200m³ 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 - Intersection 7247
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Construct
Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction, and description. - Graphically 7004
A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica
- Pieces 6890
Divide the line MN (/ MN / = 9cm) into 11 equal pieces - Isosceles 6673
Isosceles triangle X'Y'Z' . It is similar to triangle XYZ. The base of triangle XYZ has length |XY|=4cm. The size of the angle at the X vertex is 45 degrees. Draw a triangle X'Y'Z' whose base is 8 cm long. - Quadrilateral 5277
Given a regular quadrilateral pyramid ABCDV, point M is inside its edge AV, and point N is on the long line DC beyond point C. Construct the intersection of the plane MNV with the plane BCV and the intersection of the line MN and the plane BCV. - Intersect 5216
At how many points do ten lines intersect if no two are parallel? - Roof 7
The roof is a regular quadrangular pyramid with a base edge of 12 m, and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m² of the plate was?
- Trapezoid 4908
Trapezoid ABCD with bases AB = a, CD = c has height v. The point S is the center of the arm BC. Prove that the area of the ASD triangle is equal to half the area of the ABCD trapezoid. - Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Graphical 4680
Solve the system by the graphical method: x + y = 8 2x-y = 1 - Projection 4514
Draw an octagonal pyramid in free parallel projection if the length of the edge a = 3 cm and the height of the pyramid v = 6 cm. - Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
- Z9–I–1
In all nine fields of given shape to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in th - Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK is laid on it. MRAK's side length is 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until the square ca - Perpendicular 3494
In axonometry, construct the projection of a perpendicular 4-sided pyramid with a square base ABCD in the plane. The base triangle gives the axonometry. We know the center of the base S, the point of the base A, and the height of the pyramid v. - Projection 3493
In axonometry, construct a projection of an oblique circular cone with a base in a plane. The stop triangle gives dimension. We know the center of the base S, the radius of the base ra the top of the cone V, Triangle (6,7,6), S (2,0,4), V (-2,7,6), r = 3 - Circle tangent
It is given to a circle with the center S and a radius of 3.5 cm. The distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
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