Similarity — Exercises

Two similar triangles have sides in ratio $1:2$. The smaller triangle has a side of length $3$. Find the corresponding side in the larger triangle.

Triangles $ABC$ and $DEF$ are similar. $AB = 4$, $DE = 8$, $BC = 3$. Find $EF$.

Two similar triangles have corresponding sides $2$ and $6$. What is the scale factor (larger to smaller)?

Triangle $ABC \sim$ triangle $DEF$ with $\angle A = 80°$, $\angle B = 60°$. Find $\angle E$.

Two similar triangles have scale factor $3$. The smaller has area $1$. Find the area of the larger.

In triangle $ABC$, $D$ is on $AB$ with $AD = 2$, $DB = 3$. A line through $D$ parallel to $BC$ meets $AC$ at $E$ with $EC = 6$. Find $AE$.

The midsegment of a triangle connecting the midpoints of two sides is parallel to the base ($BC = 16$). Find the midsegment length.

An altitude of length $h$ is drawn to the hypotenuse of a right triangle, creating segments of length $4$ and $25$. Find $h$.

Two similar solids have scale factor $3$. The smaller has volume $1$. Find the volume of the larger.

A $18$-metre pole casts a $3$-metre shadow. At the same time, a nearby post casts a $1$-metre shadow. Find the height of the post.

Two transversals cut three parallel lines. On one transversal the segments are $8$ and $12$. On the other the first segment is $10$. Find the second segment.