Geometry Dilations and Similarity Worksheet (PDF)

Geometry math worksheet: Dilations and Similarity – Maths PDF

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This dilations practice worksheet for Geometry covers dilations and similarity (Common Core G-SRT.A.1, G-SRT.A.2, G-SRT.A.3), with a free PDF to print.

These 20 problems practice dilations, scale factors, similar figures and the AA criterion (Common Core G-SRT.A.1 to G-SRT.A.3). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are scaling, shadow and model problems.

Geometry · Common Core State Standards: G-SRT.A.1, G-SRT.A.2, G-SRT.A.3

Dilations practice worksheet: exercises 1 to 10

Exercise 1 – Dilate a point

Dilate \((3, -2)\) with center at the origin and scale factor \(3\).

Exercise 2 – Reduction

Dilate \((8, 12)\) with center at the origin and scale factor \(\frac{1}{4}\).

Exercise 3 – Dilate a triangle

Triangle ABC.

Triangle ABC has A(1, 1), B(3, 1) and C(1, 4). Dilate it with center at the origin and scale factor 2. Give the image vertices.

Exercise 4 – Shrinking a poster

A dilation shrinks a poster that is 24 inches wide to an image that is 9 inches wide. State the scale factor as a decimal, then give the height of the image when the original poster is 40 inches tall.

Exercise 5 – Find the scale factor

Triangle ABC and its image.

Side AB measures 6 and its image A′B′ measures 15. Find the scale factor of the dilation.

Exercise 6 – Enlargement or reduction?

Tell whether each scale factor gives an enlargement, a reduction, or a congruent image: \(1.4\), \(0.6\), \(1\).

Exercise 7 – Different center

Dilate \(P(4, 3)\) with center \(C(1, 1)\) and scale factor \(2\).

Exercise 8 – Reduction about a center

Dilate \(A(5, 6)\) with center \(P(2, 3)\) and scale factor \(\frac{1}{3}\).

Exercise 9 – Image of a line

A line not through the center maps to a parallel line.

The line \(y = 2x + 3\) is dilated with center at the origin and scale factor 3. Find an equation of the image.

Exercise 10 – Line through the center

The line \(y = x\) is dilated with center at the origin and scale factor 4. Describe the image.

Exercises 11 and up

Exercise 11 – Angles are preserved

Triangle ABC has \(m\angle A = 50^{\circ}\). It is dilated by a scale factor of 2.5 to give A′B′C′. Find \(m\angle A^{\prime}\) and the ratio \(\frac{A^{\prime}B^{\prime}}{AB}\).

Exercise 12 – AA similarity

Triangle 1 has angles of \(50^{\circ}\) and \(60^{\circ}\). Triangle 2 has angles of \(70^{\circ}\) and \(60^{\circ}\). Are the triangles similar? Explain.

Exercise 13 – Missing side

Triangle ABC is similar to triangle DEF.

Triangle ABC is similar to triangle DEF. AB = 6, DE = 9 and BC = 8. Find EF.

Exercise 14 – Area under dilation

A triangle has area 10 square units. Find the area of its image under a dilation with scale factor 3.

Exercise 15 – Perimeter under dilation

A triangle has a perimeter of 24 cm. Find the perimeter and the area ratio for a similar triangle with scale factor 1.5.

Exercise 16 – Third angle by AA

Triangle ABC has \(m\angle A = 48^{\circ}\) and \(m\angle B = 62^{\circ}\). Triangle DEF has \(m\angle D = 48^{\circ}\) and \(m\angle E = 62^{\circ}\). Show the triangles are similar and find \(m\angle C\) and \(m\angle F\).

Exercise 17 – Dilation then reflection

Triangle ABC has A(1, 1), B(3, 1) and C(1, 4). It is dilated by scale factor 2 about the origin and then reflected across the y-axis. Find A″, B″ and C″ and explain why the final triangle is similar to ABC.

Exercise 18 – Shadow problem

Similar right triangles.

Diego is 6 feet tall and casts a 4-foot shadow. At the same time a tree casts an 18-foot shadow. Find the height of the tree.

Exercise 19 – Photo enlargement

A 4-inch by 6-inch photo is enlarged with scale factor 2.5. Find the new dimensions and the ratio of the new area to the original area.

Exercise 20 – Model car

A toy model is built at scale 1 : 18. The real car is 15 feet long. Find the model length in inches.

Key facts behind this dilations practice worksheet

Key facts

A dilation multiplies lengths by the scale factor k; with center at the origin, (x, y) goes to (kx, ky).
Dilations preserve angle measure and send lines to parallel lines.
Area is multiplied by k squared and perimeter by k.
A line through the center of dilation maps to itself.
AA: two congruent angle pairs prove triangles similar.

How to use this dilations practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the dilations practice worksheet as a PDF with the button below and keep it with your notes.

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