BASIC PROPORTION, THALES, EUCLID, PYTHAGOR

A candle placed vertically on the ground

and a stick are shown in the figure.

The shadow of the 6 cm long stick,

which is placed 12 cm away from the candle,

is 9 cm long.

After this moment, when the candle melts by 2 cm,

how long will the shadow of the stick be in centimeters?

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[AD] // [EF] // [BC]

[BD] ∩ [EF] = {K}

|EK| = 1 cm

|KF| = 6 cm

|BC| = 8 cm

According to the above data, what is |AD| = x in centimeters?

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A teacher drew the line segments AB and CD, with lengths of 1 and 2 units respectively, on the ground divided into squares given above, on the board. Then, he asked two of his students to draw two lines passing through the endpoints of these line segments separately and to mark the intersection of the lines they drew on the ground. Since the students marked different points on the ground, how many units is the distance between the points they marked?

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There is a lamp 4 meters to the right of the blue pole in the figure, and a wall 6 meters to the left. The height of this pole is 11 meters, and the height of the lamp is 15 meters. Accordingly, what is the height (h) of the shadow created by the pole on the wall?

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• 5

• 5.5

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• 6.5

Two lampposts, 8 and 12 meters long, 5 meters apart on a straight line, and a stick on the same road are shown in the figure.

The lengths of the shadows cast by the lampposts on the same side of the stick are 4 and 13 meters. Accordingly, how many meters is the stick?

• 3

• 3,6

• 4

• 4,2

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Information: The angle of incidence of a ray on a flat surface is the same as the angle of reflection from the surface. A rectangular floor made of unit squares was created by placing blue and green flat mirrors on two sides of the floor. Then, a point light source P was placed on the other side of the floor. The ray sent from this source to the green mirror hit this mirror at point A and then reflected from the blue mirror and reached the upper edge of the floor at point K. According to this, how many units is the distance between points P and K?

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An unequal-armed seesaw consists of a linear piece mounted perpendicular to the ground at point C and a 60 cm long support attached to this piece. When the A end of this seesaw placed on a flat surface as in Figure 1 touches the ground, the height of the B end from the ground is 180 cm. Accordingly, how many centimeters will the height of the A end from the ground be when the B end of the seesaw touches the ground as in Figure 2?

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Cansu stretches the elastic fixed with a pin at points A and B with her finger and forms the isosceles triangle ABC in Figure 1 and then the right triangle ABD in Figure 2 • [AB] [AD] and |AB| = 6 units • 2 ∙ |AC| = 2 ∙ |BC| = |BD| • The distance from point C to [AB] is 4 units. According to the data above, what is the value of |AD| + |BC|=?

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Above is a square in the shape of a right triangle ABC with points A, B and C. The triangle DEF inside the square is similar to the triangle ABC. |AB| = 9 units, |BC| = 15 units and |DF| = 8 units According to the above data, how many units is the distance of point D to [EF]?

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• 4,2

• 4,5

• 4,8

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[AB] [AE], [AE] [ED], [ED] [DC] |AB| = 18 cm, |AE| = |CD| = 3 cm and |ED| = 10 cm According to the data above, what is the perimeter of the shape in centimeters?

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