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Calculate missing sides in similar triangles using proportional relationships
When two triangles are similar, their corresponding sides are proportional. This means you can set up a proportion equation and use cross-multiplication to solve for unknown sides.
Write the ratio of two sides from the first triangle equal to the ratio of the corresponding sides from the second triangle: a/b = c/d
To solve a proportion, multiply diagonally across the equals sign: if a/b = c/d, then a×d = b×c
Match sides based on their relative position. The side opposite the smallest angle corresponds to the side opposite the smallest angle in the other triangle.
After cross-multiplying, isolate x by dividing both sides of the equation by the coefficient of x.
A proportion is an equation stating that two ratios are equal. In similar triangles, corresponding sides form equal ratios, allowing us to write proportions like a/b = c/d.
In the proportion a/b = c/d, cross-multiply by multiplying a×d and b×c. This gives you a×d = b×c, which you can then solve for the unknown variable.
Only similar triangles have proportional sides. If triangles aren't similar (same shape), their sides won't maintain a constant ratio, and proportions won't work.
Look for angle markings or sort sides by length. The shortest side of one triangle corresponds to the shortest of the other, and so on for medium and longest sides.
Yes, as long as they're corresponding sides. The ratio between any two pairs of corresponding sides will be the same (the scale factor).
A ratio compares two numbers (a:b or a/b). A proportion is an equation stating that two ratios are equal (a/b = c/d).
Yes, but you'll need to know at least three measurements. Set up separate proportions for each unknown side using the known scale factor.
The more precise your known measurements, the more accurate your calculated result. Round your final answer to match the precision of your input values.
Find the scale factor between similar triangles
Check if triangles are similar
Calculate and apply scale factors
Find angles in similar triangles
Check if triangles are congruent