SSS and SAS Similarity

Name:

Class:

Date:

Show your work for each problem.

1.
Which triangle is similar to a triangle with sides $2$ , $3$ and $4$ ?
1. a)4; 6; 8
2. b)4; 5; 6
3. c)3; 4; 5
4. d)4; 6; 9
2.
$\triangle ABC$ has sides $5$ , $7$ , $8$ and $\triangle DEF$ has sides $15$ , $21$ , $24$ . The triangles are similar. What is the scale factor $k$ from $\triangle ABC$ to $\triangle DEF$ ?
3.
A triangle has sides $3$ , $5$ , $6$ and another has sides $9$ , $15$ , $18$ . Check all three ratios with SSS Similarity and find the scale factor.
4.
For $\triangle ABC$ and $\triangle DEF$ you know $\frac{DE}{AB} = \frac{DF}{AC} = 2$ and $\angle A = \angle D$ . Which criterion proves that the triangles are similar?
1. a)SAS similarity
2. b)AA similarity
3. c)SSS similarity
4. d)Not enough information
5.
$\triangle ABC \sim \triangle DEF$ with scale factor $k = 2$ from $\triangle ABC$ to $\triangle DEF$ . If $AB = 6$ , how long is $DE$ ?
6.
$\triangle ABC$ has sides $8$ , $4$ , $6$ and $\triangle DEF$ has sides $9$ , $12$ , $6$ . Pair the sides correctly and find the scale factor from $\triangle ABC$ to $\triangle DEF$ .
7.
Two triangles are similar with scale factor $k = 3$ . The smaller one has an area of $5$ cm². What is the area of the larger one?
1. a)45 cm²
2. b)30 cm²
3. c)15 cm²
4. d)9 cm²
8.
Two similar triangles have scale factor $k = 2.5$ from the smaller to the larger one. The smaller triangle has a perimeter of $18$ cm. What is the perimeter of the larger triangle in cm?
9.
$\triangle ABC$ : $AB = 3$ , $AC = 5$ , $\angle A = 120°$ , $BC = 7$ . $\triangle DEF$ : $DE = 9$ , $DF = 15$ , $\angle D = 120°$ . Show that the triangles are similar and find $EF$ .
10.
$\triangle ABC$ : $AB = 6$ , $AC = 9$ , $\angle A = 40°$ . $\triangle DEF$ : $DE = 8$ , $DF = 12$ , $\angle D = 40°$ . What can you conclude?
1. a)Not enough information
2. b)Similar by SSS Similarity, $k = \frac{4}{3}$
3. c)Similar by SAS Similarity, $k = \frac{4}{3}$
4. d)Not similar, the side ratios are different
11.
$\triangle ABC$ has sides $6$ , $8$ , $10$ . A similar triangle has sides $9$ , $12$ and $x$ , where $x$ is its longest side. Find $x$ .
12.
The triangles with sides $4$ , $6$ , $9$ and $6$ , $x$ , $13.5$ are similar (sides listed from shortest to longest). Find $x$ .
13.
In $\triangle ABC$ , point $D$ lies on $AB$ and point $E$ on $AC$ . $AD = 3$ , $AB = 9$ , $AE = 4$ , $AC = 12$ and $DE = 5$ . Find $BC$ .
14.
$\triangle ABC$ : $AB = 4$ , $BC = 6$ , $\angle C = 30°$ . $\triangle DEF$ : $DE = 8$ , $EF = 12$ , $\angle F = 30°$ . Are the triangles similar?
1. a)Yes, by SAS Similarity
2. b)No, the side ratios are different
3. c)Cannot be decided: the angle is not between the two given sides
4. d)Yes, by SSS Similarity
15.
$\triangle ABC$ : $AB = 8$ , $BC = 12$ , $\angle B = 55°$ . $\triangle DEF$ : $DE = 6$ , $EF = x$ , $\angle E = 55°$ . For which value of $x$ are the triangles similar by SAS Similarity (with $AB \leftrightarrow DE$ and $BC \leftrightarrow EF$ )?
16.
$\triangle ABC$ has sides $5$ , $12$ , $13$ and a right angle between the sides $5$ and $12$ . A similar triangle $\triangle DEF$ has shortest side $15$ . Find the perimeter and then the area of $\triangle DEF$ .
17.
In $\triangle ABC$ , point $D$ lies on $AB$ and point $E$ on $AC$ . $AD = 6$ , $DB = 4$ , $AE = 9$ , $EC = 6$ and $DE = 12$ . Show that $\triangle ADE \sim \triangle ABC$ and find $BC$ .
18.
Two similar triangles have areas $20$ cm² and $45$ cm². The shortest side of the smaller triangle is $4$ cm. How long is the shortest side of the larger triangle, in cm?