# High school geometry: Similarity problems solved # Recent questions in Similarity

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ANSWERED ### Sue is starring a lawn-cutting business. Her start-up cost tot buy two lawn mowers and an edge trimmer is $665. She has figured out that she will use about$1 in gas for each lawn. If she charges \$20 per lawn what will her break-even point be?

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ANSWERED ### What are the 3 triangle similarity criteria?

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ANSWERED ### Find the volume of the described solid. A cap of a sphere with radius and height h

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ANSWERED ### Martina is building a wind chime. She has pieces of metal pipe 2, 3, 4, and 5 inches long that she is going to use to make a triangular top for the wind chime. Which combinations of three lengths will not work to make the top?

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ANSWERED ### Find the point on the line $$y=2x+3$$ that is closest to the origin.

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ANSWERED ### To prove : The similarity of $$\displaystyle\triangle{N}{R}{T}$$ with respect to $$\displaystyle\triangle{N}{S}{P}$$. Given information: Here, we have given that $$\displaystyle\overline{{{S}{P}}}$$ is altitude to $$\displaystyle\overline{{{N}{R}}}\ {\quad\text{and}\quad}\ \overline{{{R}{T}}}$$ is altitude to $$\displaystyle\overline{{{N}{S}}}$$.

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ANSWERED ### If A, B, and C are the vertices of a triangle, find $$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}$$

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ANSWERED ### To prove: The similarity of $$\displaystyle\triangle{B}{C}{D}$$ with respect to $$\displaystyle\triangle{F}{E}{D}$$. Given information: Here, we have given that $$\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{A}{E}}}\ {\quad\text{and}\quad}\ \angle{C}{B}{D}\stackrel{\sim}{=}\angle{E}{F}{D}$$

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ANSWERED ### To determine: The ratio of the sides of the triangles ABC and GHI. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

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ANSWERED ### Similar Triangles and Triginimetric Functions Use the figure below. What does similarity imply about the ratios $$\displaystyle\frac{{{B}{C}}}{{{A}{B}}},\frac{{{D}{E}}}{{{A}{D}}},{\quad\text{and}\quad}\frac{{{F}{G}}}{{{A}{F}}}$$?

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ANSWERED ### When is a rank one matrix diagonalizable? Justify your answer. What is one choice of the diagonalizing similarity? What happens when it is not diagonalizable? Justify your answer.

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ANSWERED ### Compute the similarity dimension of a strictly self-similar fractal with a replacement ratio of 5 and a scaling ratio of 4. Round to the nearest thousandth.

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ANSWERED ### If hearts are geometrically similar and the volume of blood pumped in one beat is proportional to the volume of the heart, how much more blood will a heart 5 cm wide pump in one beat than a heart that is 3cm wide?

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ANSWERED ### To prove: The congruency of $$\displaystyle\triangle{R}{K}{M}\stackrel{\sim}{=}\triangle{O}{M}{K}$$. Given information: The following information has been given $$\displaystyle\angle{M}{R}{K}=\angle{K}{O}{M}={90}^{{\circ}}$$ $$\displaystyle\angle{R}{K}{M}=\angle{O}{M}{K}$$ KM is the common chord

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ANSWERED ### To write: the name of the postulate, that justifies the given statement. Given information:In $$\displaystyle\triangle{A}{V}{B}{\quad\text{and}\quad}\triangle{N}{V}{K},\angle{A}=\angle{N}={60}^{{\circ}}$$. The given figure is as follows: Similarity
ANSWERED ### To prove:The congruency of $$\displaystyle\vec{{{M}{H}}}\stackrel{\sim}{=}\vec{{{J}{O}}}$$. Given information: The following information has been given GJKM is a rhombus $$\displaystyle\angle{J}{O}{G}=\angle{M}{H}{G}={90}^{{\circ}}$$

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ANSWERED ### To determine: Whether the triangle ABC and GHI are similar to each other. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

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ANSWERED ### A spotlight at a building corridor is fastened to a wall 8m above the floor. A lady 1.75m tall moves away from the wall at a speed of $$\displaystyle{0.75}\frac{{m}}{{s}}$$. a.)at what rate is the lenght of her shadow increasing? b.)at what speed is the tip of her shadow moving?

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ANSWERED ### To prove:The extended proportions that are needed to prove $$\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}$$ by the SSS similarity theorem. Given $$\displaystyle\triangle{R}{S}{T},\triangle{X}{Y}{Z}$$ are two triangles.
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