Understanding Similarity in Geometry

To prove: The similarity of ${\displaystyle \mathrm{△}ABC}$ with respect to ${\displaystyle \mathrm{△}PQR}$.
Given information: Here, we have given that acute angles of both right angles are congruent (${\displaystyle \Rightarrow \mathrm{\angle }ACB\stackrel{\sim }{=}\mathrm{\angle }PRQ}$)

Determine the length of z.
Given:

Complete the similarity statement.

${\displaystyle \mathrm{△}LMN\sim \mathrm{△}}$?
Given,
In
${\displaystyle \mathrm{△}MNL}$
ML=9
NL=15
MN=12
In
${\displaystyle \mathrm{△}STR}$
SR=6
ST=8
RT=10
We have to complete the similarity statement ${\displaystyle \mathrm{△}LMN\sim \mathrm{△}}$?

Which side in the smallest triangle would correspond with ${\displaystyle \overline{RS}}$ in the largest triangle?

${\displaystyle \overline{RS}}$
${\displaystyle \overline{RQ}}$
${\displaystyle \overline{QS}}$
None of the sides correspond with ${\displaystyle \overline{RS}}$

Determine the length of x in the diagram below.

State if the triangles are similar. If so state how you know they are similar and complete the similarity statement.

Are the triangle similar, if so write a similarity statement.

Can the triangles below be proven similar by the SSS Similarity Postulate? Explain.

1)No, the SSS Similarity Postulate cannot be used to prove the two triangles are similar. To use the SSS Similarity Postulate, all three corresponding sides must be known to be proportional.
2)Yes, the SSS similarity Postulate can be used to prove the two triangles are similar. The triangles have one set of congruent corresponding angles, so the SSS Similarity Postulate can be used.
3)No, the SSS Similarity Postulate cannot be used to prove the two triangles are similar. To use the SSS similarity Postulate, all three corresponding angles must be known to be congruent.
4)No, the SSS Similarity Postulate cannot be used to prove the two triangles are similar. To use the SSS Similarity Postulate, all three corresponding sides must be known to be congruent.

Identify a similarity statement for the two triangles.

1.The triangles are not similar
2.${\displaystyle \mathrm{△}TRS\sim \mathrm{△}LJK}$
3.${\displaystyle \mathrm{△}RST\sim \mathrm{△}JKL}$
4.${\displaystyle \mathrm{△}SRT\sim \mathrm{△}KLJ}$
5.${\displaystyle \mathrm{△}TSR\sim \mathrm{△}LJK}$

Complete the similarity statement for these triangles.
Triangle TDC${\displaystyle \sim }$ Triangle ?

State if the triangles in each pair are similar if so complete the similarity statement

${\displaystyle \mathrm{△}ABC\sim }$

${\displaystyle \mathrm{△}ABC\sim \mathrm{△}KJI}$.

What is the similarity ratio of ${\displaystyle \mathrm{△}ABC\to \mathrm{△}KJI}$?

Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.

Determine which method (${\displaystyle \mathrm{\forall }\stackrel{\sim }{=}\mathrm{\forall }}$, SAS Theorem of Similarity, SSS Theorem of Similarity) proves that the following triangles are similar.

Are the two triangles similar? If yes, then complete the similarity statement.
Select all that apply.
${\displaystyle \mathrm{△}BAC\sim \mathrm{△}}$? by ? similarity

The triangles are not similar.
${\displaystyle \mathrm{△}YZX}$
${\displaystyle \mathrm{△}YXZ}$
SAS similarity
SSS similarity
AA similarity

Are the triangles similar? If so, write a similarity statement for the triangles.

Determine whether the triangles are similar. If they are, write a similarity statement.

Tell which conjecture shows the triangles similar or write not similar if there is not a way to prove them similar.

Similarity Shortcut: ?

These two triangles are similar by AA similarity. The ratio of corresponding altitudes is proportional to the ratio of corresponding sides. Find the value of x.
Given,
Two triangles are similar by angle-angle similarity,

Determine the length of x.
Given: