# Geometry - examples

- 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? - Railways

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. - 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]. - 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. - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 10 cm. - Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2.}Determine the area of the trapezoid A - 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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