# Geometry - examples

- Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - Sides od triangle

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. - Tree shadow

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)? - Sun rays

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 - Diagonals

Draw a square ABCD whose diagonals have a length of 6 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 ? - Similarity

Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°? - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Line

How many parts of line divide 5 (different) points that lie on it? - Line

Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p? - Segments

Which of the pairs of numbers on the number line encloses the longest segment: ? - Plane

On how many parts divide plane 8 parallels? - Pizza master

Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible? - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - 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 17 and one cathetus long 1. - Line

Can we construct a line segment, if we know: center and one end point - Vector

Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13]. - Shadow and light

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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