# 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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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.

2021-03-10
Calculation:
Since, the side of the triangle $$\displaystyle\triangle{A}{B}{C}$$ is 75% of the side of the triangle $$\displaystyle\triangle{D}{E}{F}$$.
$$\displaystyle\frac{{{A}{B}}}{{{D}{E}}}=\frac{{{75}}}{{{100}}}$$
$$\displaystyle{A}{B}=\frac{{3}}{{4}}{D}{E}$$...(1)
and, the side of the triangle $$\displaystyle\triangle{G}{H}{I}$$ is 32% of the side of the triangle $$\displaystyle\triangle{D}{E}{F}$$.
$$\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{32}}}{{{100}}}$$
$$\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{8}}}{{{25}}}$$
$$\displaystyle{D}{E}=\frac{{{25}}}{{{8}}}{G}{H}$$...(2)
Substitute equation (1) in equation (2).
$$\displaystyle{A}{B}=\frac{{3}}{{4}}{\left(\frac{{{25}}}{{{8}}}{G}{H}\right)}$$
$$\displaystyle\frac{{{A}{B}}}{{{G}{H}}}=\frac{{{75}}}{{{32}}}$$
Therefore, the ratio of the sides of the triangles ABC and GHI is $$\displaystyle\frac{{{75}}}{{{32}}}$$.

### Relevant Questions

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.
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 $$\displaystyle\overline{{{N}{S}}}$$.
To prove: The similarity of $$\displaystyle\triangle{N}{W}{O}$$ with respect to $$\displaystyle\triangle{S}{W}{T}$$.
Given information: Here, we have given that NPRV is a parallelogram.
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 $$\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{A}{E}}}\ {\quad\text{and}\quad}\ \angle{C}{B}{D}\stackrel{\sim}{=}\angle{E}{F}{D}$$
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors $$\displaystyle\hat{{{i}}}$$ and $$\displaystyle\hat{{{j}}}$$.
1. (Enter in box 1) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+$$
5. ( Enter in box 5) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$

State the congruence relation for $$\displaystyle\triangle{A}{B}{C}\ {\quad\text{and}\quad}\ \triangle{D}{E}{F}$$.

A.SSS
B.SSA
C.AAA
D.SAS

Given $$\displaystyle\triangle{D}{E}{F}{\quad\text{and}\quad}\triangle{E}{G}{F}$$ in the diagram below, determine if the triangles are similar. If so, write a similarity statement, and state the criterion used to support your claim.
Determine whether $$\displaystyle\triangle{A}{B}{C}{\quad\text{and}\quad}\triangle{D}{E}{F}$$ are similar for each set of measures. If so, identify the similarity criterion.
1.$$\displaystyle{m}\angle{A}={20},{m}\angle{C}={20},{m}\angle{D}={40},{m}\angle{F}={40}$$
2.$$\displaystyle{m}\angle{A}={20},{m}\angle{C}={4}{u},{m}\angle{D}={20},{m}\angle{F}={40}$$
3.$$\displaystyle{A}{B}={20},{B}{C}={40},{m}\angle{B}={53}$$,
$$\displaystyle{D}{E}={10},{E}{F}={20},{m}\angle{E}={53}$$