Geometry Unit 3: Similarity

Dilations and scale factor, similar triangles, the side splitter theorem, and how perimeter, area and volume scale. 12 questions. Have a go at each one on paper before you tap "Show me how".

A free account opens the worked solutions to 20 questions a day; Pro opens every one.

Question 1

DilationsNo calculator

A dilation with scale factor 2.5 maps segment $AB$, of length 6, to $A'B'$. How long is $A'B'$?

1. $2.4$
2. $8.5$
3. $3.5$
4. $15$

Question 2

Similar trianglesNo calculator

Triangle $ABC\sim$ triangle $DEF$, with $AB=8$, $BC=12$ and $DE=10$. How long is $EF$?

1. $\frac{20}{3}$
2. $15$
3. $9.6$
4. $14$

Question 3

Similar trianglesNo calculator

A 6-foot person casts a 4-foot shadow. At the same moment, a tree casts a 30-foot shadow. How tall is the tree, in feet?

1. $32$
2. $20$
3. $45$
4. $40$

Question 4

Side splitterNo calculator

Segment $DE$ is parallel to side $BC$ of triangle $ABC$, with $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$. Given $AD=3$, $DB=9$ and $AE=4$, find $EC$.

1. $\frac{4}{3}$
2. $10$
3. $12$
4. $16$

Question 5

Area of similar figuresNo calculator

A triangle has area 12 square units. A similar triangle has sides 3 times as long. What is its area?

1. $324$
2. $48$
3. $108$
4. $36$

Question 6

Volume of similar solidsNo calculator

Two similar cylinders have radii 2 and 5. The smaller one has volume 40 cubic units. What is the volume of the larger one?

1. $250$
2. $100$
3. $1000$
4. $625$

Question 7

AA similarityNo calculator

One triangle has angles of $48^\circ$ and $61^\circ$. Another has angles of $61^\circ$ and $71^\circ$. Are the triangles similar?

1. Yes, by SSS
2. Only if one pair of sides is equal
3. No, the third angles differ
4. Yes, by AA

Question 8

Right triangle similarityNo calculator

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of 4 and 9. How long is the altitude?

1. $6.5$
2. $13$
3. $6$
4. $36$

Question 9

DilationsNo calculator

A dilation centered at $(1,1)$ with scale factor 3 is applied to the point $(3,2)$. What is the image?

1. $(5,4)$
2. $(7,4)$
3. $(9,6)$
4. $(6,3)$

Question 10

Scale drawingsNo calculator

On a map, 1 inch represents 25 miles. Two towns are 3.4 inches apart on the map. How far apart are they, in miles?

1. $7.35$
2. $850$
3. $28.4$
4. $85$

Question 11

Scale factorNo calculator

Triangle $PQR\sim$ triangle $STU$ with $PQ=9$ and $ST=6$. What is the scale factor from $PQR$ to $STU$?

1. $\frac{2}{3}$
2. $3$
3. $\frac{1}{3}$
4. $\frac{3}{2}$

Question 12

Perimeter of similar figuresNo calculator

Two similar pentagons have corresponding sides of 4 and 10. The smaller pentagon has perimeter 26. What is the perimeter of the larger one?

1. $10.4$
2. $65$
3. $162.5$
4. $32$