Geometry construction - high school - practice problems
Number of problems found: 46
- 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). - Hypotenuse 82370
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°. - Circumscribing 80498
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 - Triangle 73464
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.
- Construct 61253
Using Euclid's theorem, construct a line of length √15. - Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure. - Square equal rhombus
Construct a square that has the same area as a rhombus ABCD if |AB| = 5cm, |AD| = 4cm and angle |DAB| = 30°. - Half-planes 36831
The line p and the two inner points of one of the half-planes determined by the line p are given. Find point X on the line p so that the sum of its distances from points A and B is the smallest. - Calculate 35083
Draw an isosceles triangle ABC with a base 7 cm long and shoulders 5.5 cm long. Assemble all the heights, measure them, and calculate their sum.
- As shown
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE - Vertex points
Suppose the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - (diagonal) 30621
The ABCD diamond shape we known diagonal u2 and a height v. Do an analysis. - Larger perimeter
A square and a circle pass through two adjacent vertices of the square (endpoints of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter? - Construction 27743
The length of the gutter is 2 m, and the diameter of the gutter is 0.4 m. It is necessary to add 7% of the material to the joints. Find the consumption of sheet metal for the gutter construction.
- Meneal's 26771
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - 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. ) - 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 11511
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 options - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b.
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