8th Grade Math · Similar Triangles Find a missing side Worksheets
Triangle ABC ∼ triangle DEF, drawn to scale. Students match up the sides and find x, such as 7.5 cm.
Make it yours
6 problems · 1 page, plus an answer key
Or print a ready-made one (6 problems · 1 page): worksheet · answer key
How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| Angle sum | The three angles of every triangle add up to 180°. |
| Angle-angle (AA) | If two angles of one triangle equal two angles of another, the triangles are similar. |
| Matching sides | In triangle ABC ∼ triangle DEF, A matches D, B matches E and C matches F, so AB matches DE. |
| Scale factor | Divide a side of one triangle by its matching side in the other. Every pair of matching sides gives the same number. |
| Shadows | Height ÷ shadow is the same for everything at the same time of day. |
Worked example
A tree casts a 60-inch shadow at the same time that a 68-inch student casts a 17-inch shadow. How tall is the tree, in feet?
- 1The tree and its shadow, and the student and their shadow, form similar right triangles.
- 2Set up a proportion: tree ÷ 60 = 68 ÷ 17.
- 368 ÷ 17 = 4, so the tree is 4 times its shadow: 4 × 60 = 240 inches.
- 4There are 12 inches in a foot: 240 ÷ 12 = 20, so the tree is 20 feet tall.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Find a missing side Worksheets, version 1Worksheet PDFAnswer key PDF
- Find a missing side Worksheets, version 2Worksheet PDFAnswer key PDF
- Find a missing side Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (geometry). It practices what Common Core standard CCSS 8.G.A.5 describes, and also works as review in later grades. How we check standards and answers
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet code printed at the bottom of each page pairs a sheet with its key.
- Are the triangles drawn to scale?
- Yes. Every triangle is drawn from its true angles or side lengths, and the two triangles in a problem share one scale, so the bigger one really is bigger.
- Why does the angle-angle test only need two angles?
- The three angles always add up to 180°, so once two angles match, the third must match too. Triangles with the same three angles have the same shape: they are similar.
- Are similar triangles also congruent?
- Only when the scale factor is 1. Similar triangles have the same shape; congruent triangles have the same shape and the same size.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.
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