Georgia Milestones Geometry Similarity, Right Triangles, and Trigonometry Practice

What the test measures

Similarity, Right Triangles, and Trigonometry skills

Understand similarity in terms of similarity transformations
Prove theorems involving similarity
Define trigonometric ratios and solve problems involving right triangles

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Official sources

Georgia Department of Education

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Each exterior angle of a regular polygon measures $30^{\circ}$ . How many sides does the polygon have?

The exterior angles of any convex polygon sum to $360^{\circ}$ . For a regular polygon, $n \cdot 30^{\circ} = 360^{\circ}$ , so $n = 12$ .

Practice playeasy

In a right triangle, $\cos\theta = \dfrac{12}{13}$ and $\tan\theta = \dfrac{5}{12}$ . What is $\sin\theta$ ?

$\sin\theta = \tan\theta \cdot \cos\theta = \dfrac{5}{12} \cdot \dfrac{12}{13} = \dfrac{5}{13}$ .

Practice playeasy

A $3$ -foot fence post casts a shadow $2$ feet long. At the same time, a telephone pole casts a shadow $28$ feet long. How tall is the telephone pole, in feet?

Use $\dfrac{3}{2} = \dfrac{h}{28}$ . Cross-multiply: $2h = 84$ , so $h = 42$ feet.

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $7$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $7$ .

Practice playeasy

Two similar triangles have perimeters in the ratio $3 : 5$ . The shortest side of the smaller triangle is $6$ . What is the length of the shortest side of the larger triangle if corresponding sides are compared?

Similar figures have a constant scale factor between corresponding lengths. Perimeter ratio $3 : 5$ means each side of the larger triangle is $\dfrac{5}{3}$ times the matching side of the smaller. The larger shortest side is $6 \cdot \dfrac{5}{3} = 10$ .

Practice playeasy

In a right triangle, $\cos\alpha = \dfrac{24}{25}$ and $\tan\alpha = \dfrac{7}{24}$ . What is $\sin\alpha$ ?

$\sin\alpha = \tan\alpha \cdot \cos\alpha = \dfrac{7}{24} \cdot \dfrac{24}{25} = \dfrac{7}{25}$ .

Practice playeasy

A person who is $5$ feet tall casts a shadow $3$ feet long. At the same time, a water tower casts a shadow $24$ feet long. How tall is the water tower, in feet?