Understanding Similarity in Geometry

Determine the length of y.
Given:

Can the triangles below be proven similar by the SAS Similarity Postulate?

Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are proportional, and the included angles by these sides are congruent.
Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are congruent, and the included angles by these sides are congruent.
No, the SAS Similarity Postulate cannot be used because the corresponding angles are congruent but not included by the proportional sides.
No, the SAS Similarity Postulate cannot be used because the 2 sets of corresponding sides are not proportional.

Determine whatever each pair if figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.

Are the two triangles similar? If so, by what similarity shortcut?

SSS
SAS
AA
Not Similar

Complete the similarity statement.

${\displaystyle \mathrm{△}CBA\sim }$?

Triangle ABC Triangle FDE are similar. What is the similarity ratio from triangle ABC to FDE?

Which similarity shortcut allows you to answer the value for h and k?

h=?, k=?

Which property of similarity can be used to prove triangles PQR and STU are similar?

1)SAS
2)not enough information
3)AA
4)SSS

Determine if the triangles below are similar. If so, then complete the similarity statement.

${\displaystyle \mathrm{△}JKL\sim }$?
a)Not similar
b)${\displaystyle \mathrm{△}JED}$
c)${\displaystyle \mathrm{△}DJE}$
d)${\displaystyle \mathrm{△}EJD}$

Determine if the figures are similar. If they are, write the similarity statement and find the scale factor.

In the diagram, ${\displaystyle \mathrm{△}ABC\sim \mathrm{△}DEF}$.

If AB=6 and AC=8, which statement will justify similarity by SAS?
1) DE=9, DF=12, and ${\displaystyle \mathrm{\angle }A\stackrel{\sim }{=}\mathrm{\angle }D}$
2) DE=8, DF=10, and ${\displaystyle \mathrm{\angle }A\stackrel{\sim }{=}\mathrm{\angle }D}$
3) DE=36, DF=64, and ${\displaystyle \mathrm{\angle }C\stackrel{\sim }{=}\mathrm{\angle }F}$
4) DE=15, DF=20, and ${\displaystyle \mathrm{\angle }C\stackrel{\sim }{=}\mathrm{\angle }F}$

Tell whether the pair of triangles below is similar and give the reason.

Yes, using the Side-Side-Side (SSS) similarity theorem
Yes, using the Angle-Angle (AA) similarity postulate
No, the triangles are not similar
Yes, using the Side-Angle-Side (SAS) similarity theorem

Determine (if possible) the similarity postulate that proves the following two triangles are similar:

SAS similarity postulate
AA similarity postulate
SSS similarity postulate
These triangles are not similar

${\displaystyle \mathrm{△}KLM\sim }$?
A)similar, SSS similarity. ${\displaystyle \mathrm{△}RKS}$
B)similar. SAS similarity. ${\displaystyle \mathrm{△}KRS}$
C)not similar
D)similar. SAS similarity. ${\displaystyle \mathrm{△}RKS}$

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?

What are the 3 triangle similarity criteria?

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

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?

To prove : The similarity of ${\displaystyle \mathrm{△}NRT}$ with respect to ${\displaystyle \mathrm{△}NSP}$.
Given information: Here, we have given that ${\displaystyle \overline{SP}}$ is altitude to ${\displaystyle \overline{NR}\text{and}\overline{RT}}$ is altitude to ${\displaystyle \overline{NS}}$.