# Similarity of triangles - practice problems

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 139

- 12cm 4365

a = 6cm, b = 8cm, c =? , a '=? , b '= 12cm, c' = 15cm - Catheti

One of the catheti of the right triangle has a length of 12 cm. At what distance from the center of the hypotenuse is another cathetus? - Similarity coefficient

The triangles ABC and A'B'C' are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A'B'C'. - Triangles 6647

For triangles ABC and A'B'C': alpha = alpha with a line, beta with line = beta. a) are these triangles identical? Why? b) are these triangles similar? Why? - The triangles

The triangles ABC and A'B'C 'are similar, with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35° and beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - Two angles

The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees. - Similarity of triangles

If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place. - Similarity

Are two right triangles similar if the first one has an acute angle 70° and the second one has an acute angle 20°? - The straight

The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m? - The triangles

Two similar triangles, KLM and ABC, are given. Calculate the lengths of the remaining sides of the triangle KLM. If the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5 - Similarity

ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity. - Cosine

Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544. - See harmonics

Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - Following 6660

KLM triangle on sides k = 5.4 cm. L = 6 cm, m = 6.6 cm. Construct a triangle K 'L'M 'for which the following holds: ∆KLM ~ ∆K 'L'M' and m '= 9.9cm - Figure 2

Figure A maps to figure B with a scale factor of 0.75. The length of the line AB segment in figure A is 10. What is its length on the image in figure B? - Tree shadow

The shadow of the tree is 16 meters long. The shadow of a two-meter-high tourist sign beside standing is 3.2 meters long. What height has a tree (in meters)? - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Climb

The road has climbing 1:27. How big is an angle correspond to this climbing? - Coefficient 4872

Find out if the triangles ABC and A'B'C' are similar, determine the similarity coefficient and write the similarity: a = 40 mm, b = 48 mm, c = 32 mm a´ = 60 mm, b´ = 50 mm, c´ = 40 mm - Determine 80754

The perimeter of triangle MAK is 216 mm, side a = 81 mm, and side k = 62 mm. Determine the side length of the triangle OSA if the triangle MAK is congruent to the triangle OSA.

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