Geometry - examples
Divide the three line segment 13 cm, 26 cm and 19.5 cm long for parts so that the individual parts were equally long and longest. How long will the individual parts and how many it will?
- Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
- Tree shadow
Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
- 2d shape
Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm.
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
Is right that in any right triangle height is less or equal half of the hypotenuse?
How many parts of line divide 5 (different) points that lie on it?
Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
Which of the pairs of numbers on the number line encloses the longest segment: ?
On how many parts divide plane 8 parallels?
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
- Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
- Linear independence
Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
- OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 8 and one cathetus long 4.
Can we construct a line segment, if we know: center and one end point
Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
- See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.