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: 185
- Lamp shade
A lamp shade is in the form of a frustum of a cone with slant height 7 in., radii of bases 3 in. and 7 in. respectively. How much material is used in its construction if ¼ in. 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=7cm, e=5 cm. - Diagonals
Construct a rhombus whose diagonals have lengths of 10cm and 8cm and make an angle of 115°. - Semicircles
In a rectangle with sides of 4cm and 8cm, there are two different semicircles, each of which has its endpoints at its adjacent vertices and touches the opposite side. Construct a square such that its two vertices lie on one semicircle, the remaining two o - 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: - 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 = 8cm and the length of the diagonal AC is 13cm. Measure the length of the sides of the rectangle. - Sss triangle 2
Construct triangle ABC in which |AB|=5cm, |AC|=6cm and |BC|=9cm - 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 7cm. - 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 sides
Construct triangle KLM if side m=6.5cm, hypotenuse tm=4cm, height to side m: vm=3.2cm - Triangle - BAC angle
The given line is a BC length of 6 cm. Construct a triangle so that the BAC angle is 50° and the height to the side is 5.5 cm. Thank you very much.
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