Geometry - examples

  1. Quadrilateral 2
    quadrilateral Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
  2. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  3. Sides od triangle
    podobnost Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
  4. Tree shadow
    tree3 The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
  5. Sun rays
    sfinga-a-cheopsova-pyramida-w-4066 If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
  6. Diagonals
    stvorec_7 Draw a square ABCD whose diagonals have a length of 6 cm
  7. Reverse Pythagorean theorem
    pytagors 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 ?
  8. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
  9. Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  10. Line
    line_points How many parts of line divide 5 (different) points that lie on it?
  11. Line
    img2 Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
  12. Segments
    abs Which of the pairs of numbers on the number line encloses the longest segment: ?
  13. Plane
    rovnobezky On how many parts divide plane 8 parallels?
  14. Pizza master
    pizza_3 Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
  15. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  16. Linear independence
    colinear_vectors Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
  17. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 17 and one cathetus long 1.
  18. Line
    line Can we construct a line segment, if we know: center and one end point
  19. Vector
    vectors Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
  20. Shadow and light
    stin Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?

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