Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

Rui Baldwin 2021-08-01 Answered
Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.
image

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Nathanael Webber
Answered 2021-08-02 Author has 21884 answers
In the triangle BCD,
\(\displaystyle\angle{B}={88}^{{\circ}}\)
\(\displaystyle\angle{D}={49}^{{\circ}}\)
\(\displaystyle\angle{C}={180}^{{\circ}}-{\left({88}^{{\circ}}+{49}^{{\circ}}\right)}\)
\(\displaystyle={43}^{{\circ}}\)
In the triangle IJH,
\(\displaystyle\angle{I}={43}^{{\circ}}\)
\(\displaystyle\angle{J}={49}^{{\circ}}\)
\(\displaystyle\angle{H}={180}^{{\circ}}-{\left({43}^{{\circ}}+{49}^{{\circ}}\right)}\)
\(\displaystyle={88}^{{\circ}}\)
Then, \(\displaystyle\angle{B}=\angle{H},\angle{D}=\angle{J},\angle{C}=\angle{I}\)
So, two triangles BCD and IJH will be similar if \(\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{C}{D}}}{{{I}{J}}}}\)
Now,
\(\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{6}}}{{{4}}}}\)
\(\displaystyle={\frac{{{3}}}{{{2}}}}\)
\(\displaystyle{\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{9}}}{{{6}}}}\)
\(\displaystyle={\frac{{{3}}}{{{2}}}}\)
\(\displaystyle{\frac{{{C}{D}}}{{{I}{J}}}}={\frac{{{12}}}{{{8}}}}\)
\(\displaystyle={\frac{{{3}}}{{{2}}}}\)
Since \(\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{C}{D}}}{{{I}{J}}}}\), triangle BCD and HIJ are similar.
Not exactly what you’re looking for?
Ask My Question
11
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-11
Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.
asked 2021-08-01

Determine whether the polygons to the right are similar. If so, write a similarity statement and give the scale factor. If not, explain.
image
A.Tes, \(\displaystyle\triangle{M}{N}{P}\sim\triangle{V}{W}{X}\). The scale factor is ?.(Type an integer or a simplified fraction.)
B.No, because lengths of corresponding sides are not proportional.
C.Yes, \(\displaystyle\triangle{M}{N}{P}\sim\triangle{X}{V}{W}\). The scale facor is ?.(Type an integer or a simplified fraction.)
D.No, because corresponding angles are not congruent.
E.Yes, \(\displaystyle\triangle{M}{N}{P}\sim\triangle{W}{X}{V}\). The scale factor is ?.(Type an integer or a simplified fraction.)
F.Yes, \(\displaystyle\triangle{M}{N}{P}\sim\triangle{V}{X}{W}\). The scale factor is ?.(Type an integer or a simplified fraction.)

asked 2021-08-08
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor.
asked 2021-08-05
Determine whatever each pair if figures is similar. If so, write the similarity statement and scale factor.
asked 2021-07-31
Determine whatever each pair if figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.
asked 2021-07-30
Determine if the figures are similar. If they are, write the similarity statement and find the scale factor.
asked 2021-08-11
Determine whether the triangles are similar. If so, wrote the similarity statement and name the postulate or theorem you used.
...