Geometry Dilations and Similarity Test with Point Values (PDF)

Geometry math test: Dilations and Similarity – Maths PDF

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This dilations test 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.

This 45-minute test checks dilations on the coordinate plane and similar figures. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Dilations and Similarity
Standards: G-SRT.A.1, G-SRT.A.2, G-SRT.A.3
Time: 45 minutes
Total: 20 points

Dilations test: questions

Question 1 – Dilate a rectangle [2 pts]

Rectangle ABCD.

Dilate rectangle ABCD with center at the origin and scale factor 2. Give the image vertices and compare the areas.

Question 2 – Center not at the origin [2 pts]

Dilate the point (6, 2) with center (2, 2) and scale factor 3/2. Then dilate (6, 2) with center (2, 2) and scale factor 3.

Question 3 – True or false [3 pts]

A dilation always preserves angle measure. (1 point)
A dilation with scale factor 4 turns a line not through the center into a perpendicular line. (1 point)
A dilation with scale factor 3 multiplies area by 9. (1 point)

Question 4 – Similar triangles [2 pts]

Triangles ABC and DEF.

The triangles are similar. Find the scale factor from ABC to DEF and the length of EF.

Question 5 – AA [2 pts]

Triangle PQR has angles of 35° and 80°. Triangle XYZ has angles of 65° and 80°. Are they similar? Show the work.

Question 6 – Proportions with x [3 pts]

Triangle ABC is similar to triangle DEF with AB = 9, BC = x + 2, DE = 6 and EF = 8. Find x, then find the scale factor from DEF to ABC, then find the perimeter of ABC if AC = 15.

Question 7 – Area and perimeter [2 pts]

Two similar polygons have a scale factor of 4 : 5 (small to large). The small polygon has perimeter 36 and area 40. Find the perimeter and the area of the large polygon.

Question 8 – Flagpole shadow [2 pts]

Student and flagpole.

A 5-foot-tall student casts a 7.5-foot shadow. A flagpole casts a 30-foot shadow at the same time. Find the height of the flagpole.

Question 9 – Scale model [2 pts]

A scale model of a bridge uses the scale 1 : 40. The real bridge is 120 feet long and 30 feet tall. Find the model’s length and height in feet.

Key facts behind this dilations test

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 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 Geometry chapters: Geometry math.

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