Worksheets: similarity and thalesPlane geometry · high school

A quiz in groups or a practice sheet on “Similarity and Thales” - with an answer key, ready to print, free. You can combine it with other sections.

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Answer key · group A · for the teacher · sheet no. 204 517

Similarity and Thales

1.1811 : 9 = 19 ;1 · 1 = 1, 9 · 9 = 81

2.21 cm63 : 45 = 75 ;15 · 75 = 21

3.5353 · 53 = 259

4.12 cm16 · 9 = 144 ;√144 = 12

5.120 cm64 : 8 = 8 ;15 · 8 = 120

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Answer key

Quiz

Similarity and Thales

GroupAB

Name Date Score / 17

1.Give the ratio of the areas.Two similar figures have their sides in the ratio 9 : 10. What is the ratio of the area of the second one to the area of the first?(3 pt)

2.Compute the length.Two triangles are similar. In the first one two sides are 4 cm and 2 cm. In the second one the side corresponding to the first of them is 8 cm. How long is the side corresponding to the second one?(3 pt)

3.Find the perimeter of the figure.Triangle KLM is similar to triangle ABC with scale factor 4/3, that is, each side of KLM is 43 times the corresponding side of ABC. The perimeter of ABC is 30 cm. What is the perimeter of KLM?(2 pt)

4.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). |CD| = 10 cm, |AD| = 5 cm. How long is the segment BD?(3 pt)

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Group B

Quiz

Similarity and Thales

GroupAB

Name Date Score / 17

1.Give the ratio of the areas.Two similar figures have their sides in the ratio 9 : 1. What is the ratio of the area of the second one to the area of the first?(3 pt)

2.Compute the length.Two triangles are similar. In the first one two sides are 45 cm and 15 cm. In the second one the side corresponding to the first of them is 63 cm. How long is the side corresponding to the second one?(3 pt)

3.Give the ratio of the perimeters.The areas of two similar figures are in the ratio 25 : 9. What is the ratio of the perimeter of the first figure to the perimeter of the second?(2 pt)

4.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). |AD| = 16 cm, |BD| = 9 cm. How long is the altitude CD?(3 pt)

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Group A

Sheet settings

Quiz6 questions2 groups1 topic

Sheet no.204 517The number is only shown here and on the answer key - never on the student sheet. The same number with the same topics gives the same sheet.

answer key at the endall groups

Quiz

Similarity and Thales

GroupAB

Name Date Score / 17

1.Give the ratio of the areas.Two similar figures have their sides in the ratio 9 : 1. What is the ratio of the area of the second one to the area of the first?(3 pt)

3.Give the ratio of the perimeters.The areas of two similar figures are in the ratio 25 : 9. What is the ratio of the perimeter of the first figure to the perimeter of the second?(2 pt)

5.Compute the length.Two parallel lines cut the arms of an angle. On the first arm they cut off segments of 8 cm and 64 cm. On the second arm the segment corresponding to the first one is 15 cm. How long is the other one?(3 pt)

6.Find the length of the segment.In triangle ABC the bisector of angle ACB meets side AB at the point D. |AD| = 6 cm, |DB| = 8 cm, |AC| = 18 cm. How long is the side BC?(3 pt)

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Answer key · group A · for the teacher · sheet no. 204 517

Similarity and Thales

1.1811 : 9 = 19 ;1 · 1 = 1, 9 · 9 = 81

2.21 cm63 : 45 = 75 ;15 · 75 = 21

3.5353 · 53 = 259

4.12 cm16 · 9 = 144 ;√144 = 12

5.120 cm64 : 8 = 8 ;15 · 8 = 120

6.24 cm18 · 8 : 6 = 24

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Quiz

Similarity and Thales

GroupAB

Name Date Score / 17

1.Give the ratio of the areas.Two similar figures have their sides in the ratio 9 : 10. What is the ratio of the area of the second one to the area of the first?(3 pt)

5.Compute the length.Two parallel lines cut the arms of an angle. On the first arm they cut off segments of 18 cm and 90 cm. On the second arm the segment corresponding to the first one is 5 cm. How long is the other one?(3 pt)

6.Find the length of the segment.In triangle ABC the bisector of angle ACB meets side AB at the point D. |AD| = 3 cm, |DB| = 4 cm, |BC| = 20 cm. How long is the side AC?(3 pt)

Maths worksheets · phiboard.compage 10 of 10

Answer key · group B · for the teacher · sheet no. 204 517

Similarity and Thales

1.1008110 : 9 = 109 ;10 · 10 = 100, 9 · 9 = 81

2.4 cm8 : 4 = 2 ;2 · 2 = 4

3.40 cm30 · 43 = 40

4.20 cm10² : 5 = 20

5.25 cm90 : 18 = 5 ;5 · 5 = 25

6.15 cm20 · 3 : 4 = 15

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

What goes on the sheet: similarity and thales

The generator draws questions from 6 question types in this topic. Every quiz group gets the same types in the same order, only with different numbers, and a practice sheet goes from easier to harder.

Perimeters and areas of similar figures
The intercept theorem
Similar triangles
Ratio of areas of similar figures
The angle bisector theorem
The altitude and segments in a right triangle

What the section covers in the curriculum: angles of an isosceles triangle, the Pythagorean theorem, similar triangles and the ratio of areas of similar figures, the intercept theorem, inscribed and central angles, tangents to a circle, the circumcircle of a right triangle, angles in quadrilaterals, regular polygons, areas of quadrilaterals, area and circumference of a circle, sectors, justifying steps of reasoning

Students can also practise online - the same question types, with step-by-step solutions: Exercises: similarity and thales →

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