8th Grade Dilations and Similar Figures Test with Point Values (PDF)

8th Grade math test: Dilations and Similar Figures – Maths PDF

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This dilations similarity test for 8th Grade covers dilations and similar figures (Common Core 8.G.A.3, 8.G.A.4), with a free PDF to print.

This 20-point test checks dilations, scale factors, similar figures and similarity transformations (Common Core 8.G.A.3 and 8.G.A.4). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Dilations and Similar Figures
Standards: 8.G.A.3, 8.G.A.4
Time: 45 minutes
Total: 20 points

Dilations similarity test: questions

Question 1 – Dilate points [2 pts]

Dilate \((3, -5)\) from the origin by scale factor 4. (1 point)
Dilate \((12, 8)\) from the origin by scale factor \(\frac{1}{4}\). (1 point)

Question 2 – Dilate a figure [3 pts]

Triangle KLM.

Dilate triangle \(KLM\) from the origin with scale factor 2. List the image vertices.

Question 3 – Scale factor [2 pts]

Each side of the large triangle is 2 times the matching side.

The triangles are similar. Find the scale factor from the small to the large triangle, and the perimeter of the large triangle if the small one has perimeter 12.

Question 4 – Missing length [3 pts]

Triangle \(DEF\) is similar to triangle \(GHI\). \(DE = 5\), \(EF = 7\), and \(GH = 15\). Find \(HI\).

Question 5 – Tree height [3 pts]

Sun rays make similar right triangles.

A 5-foot student casts a 3-foot shadow. A flagpole casts a 12-foot shadow at the same time. How tall is the flagpole?

Question 6 – Area [2 pts]

A square has side 5 cm. It is dilated with scale factor 3. Find the area of the image and compare it to the original area.

Question 7 – Describe a sequence [3 pts]

Triangle ABC and its image.

Describe a sequence of transformations that maps \(ABC\) to \(A^{\prime}B^{\prime}C^{\prime}\).

Question 8 – Explain [2 pts]

Explain how similar figures differ from congruent figures. Use the words angles and lengths.

Key facts behind this dilations similarity test

Key facts

Dilation from the origin: \((x, y) \to (kx, ky)\).
\(k > 1\) enlarges; \(0 < k < 1\) reduces; \(k = 1\) leaves the figure unchanged.
Angles stay equal; side lengths multiply by \(k\); area multiplies by \(k^{2}\).
Similar figures have equal angles and proportional sides.
Use \(\frac{\text{new}}{\text{old}} = k\) to find missing lengths.

How to use this dilations similarity test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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