Geometry construction - practice problems
Geometry construction problems involve creating precise geometric figures using only specific tools, classically a compass (for drawing circles and arcs) and straightedge (for drawing straight lines without measurement). Fundamental constructions include bisecting angles and segments, constructing perpendicular and parallel lines, copying angles, and creating regular polygons. These constructions must be exact, not approximations from measurement. Historical problems include the three classical impossible constructions: squaring the circle, doubling the cube, and trisecting an angle using only compass and straightedge. Modern geometric constructions also use other tools and appear in applications like computer-aided design. Construction problems develop spatial reasoning, logical thinking, and understanding of geometric relationships and properties.Number of problems found: 189
- Lamp shade
A lampshade is in the form of a frustum of a cone with a slant height of 7 inches and base radii of 3 inches and 7 inches respectively. How much material is used in its construction if 1/4 inch is allowed for the seam? - RST triangle
Find out if it is possible to construct the given triangle and according to which theorem: RS = 2.5 cm ST = 7 cm TR = 4.5 cm - Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - Construct 22
Construct a rhombus ABCD if the diagonals are f = 7 cm and e = 5 cm. - Diagonals
Construct a rhombus whose diagonals have lengths of 10 cm and 8 cm and make an angle of 115° with each other. - Semicircles
In a rectangle with sides of 4 cm and 8 cm, there are two different semicircles, each with its endpoints at adjacent vertices and touching the opposite side. Construct a square such that two of its vertices lie on one semicircle, the other two vertices li - Construction - Euclid
Using Euclid's theorems, construct a triangle ABC with height on side c and size v = √8 cm. Choose the length of the hypotenuse c correctly. Write the construction procedure. - Triangle construction progress
An isosceles triangle ABY has a base AB of length 5 cm and an angle at the primary vertex of 50°. Write down the construction progress. - Circle chord construction
Two line segments of different lengths are given. Construct a circle k so that both line segments are its chords. - Circle construction points Construct 2 circles so that their centers are 5 cm apart and: and they had no common touch b- they had a common point They had 2 points in common.
- Hypotenuse - construct problem
A line segment AA1 of length 6 cm is given. Construct all triangles ABC for which AA1 is the hypotenuse, side length BC is 5 cm, and angle gamma is 60°. - Rhombus construction sides
Construct a rhombus that has a side length of 5 cm and a height of 4.5 cm. Outline: Analysis: Construction: Method: - General trapezoid
In general trapezoid VLAK, the following are given: |VL| = 5.5 cm; |VK| = 3.5 cm; |LK| = 4.8 cm; |∠VLA| = 70°. Divide it into two triangles by drawing a diagonal. Label the newly created points. Write down the lengths of the line segments. Complete the co - Parallelogram diagonal construction
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Rectangle construction diagonal
Construct a rectangle ABCD if a = 8 cm and the length of the diagonal AC is 13 cm. Measure the length of the sides of the rectangle. - Sss triangle 2
Construct triangle ABC in which |AB|=5 cm, |AC|=6 cm and |BC|=9 cm - Triangle circle proof Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri
- Square diagonal drawing
Draw a square EFIJ if EI is equal to 7 cm. - Square point distance
I was given a square ABCD 4.2 cm. Find the set of all points that have a distance less than or equal to 2 cm from one of its vertices and lie inside this square. Indicate how much of the square this area occupies as a percentage. - Triangle construction
Construct triangle KLM if side m=6.5 cm, median to the side m tm=4 cm, height to side m: vm=3.2 cm
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