Similarity and Thales
Types of exercises: the intercept theorem, similar triangles, ratio of areas of similar figures, perimeters and areas of similar figures, the angle bisector theorem, the altitude and segments in a right triangle.
Exercises are drawn at random from a large bank - every click gives a different set.
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Compute the length
Two parallel lines cut the arms of an angle. On the first arm they cut off segments of 10 cm and 80 cm. On the second arm the segment corresponding to the first one is 19 cm. How long is the other one?
Find the area of the figure
Two similar figures have perimeters of 4 cm and 20 cm. The area of the first one is 6 cm². What is the area of the second one?
Find the length of the segment
In triangle ABC the bisector of angle ACB meets side AB at the point D. |AC| = 18 cm, |BC| = 15 cm, |AB| = 22 cm. How long is the segment DB?
Give the ratio of the areas
Two similar figures have their sides in the ratio 3 : 4. What is the ratio of the area of the second one to the area of the first?
Compute the length
Two triangles are similar. In the first one two sides are 32 cm and 64 cm. In the second one the side corresponding to the first of them is 20 cm. How long is the side corresponding to the second one?
Find the length of the segment
CD is the altitude of the right triangle ABC with the right angle at C (the point D lies on the hypotenuse AB). |AB| = 36 cm, |AD| = 32 cm. How long is the leg BC?
Compute the length
Two parallel lines cut the arms of an angle. On the first arm they cut off segments of 7 cm and 14 cm. On the second arm the segment corresponding to the first one is 2 cm. How long is the other one?
Give the ratio of the perimeters
The areas of two similar figures are in the ratio 9 : 1. What is the ratio of the perimeter of the first figure to the perimeter of the second?
Find the length of the segment
In triangle ABC the bisector of angle ACB meets side AB at the point D. |AC| = 9 cm, |BC| = 18 cm, |AB| = 24 cm. How long is the segment AD?
Compute the area
Two similar figures have their sides in the ratio 6 : 1. The area of the first one is 144 cm². What is the area of the second one?
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