Triangle ABC is similar to triangle DEF. Triangle DEF is similar to triangle GHI. Determine the missing...

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1. Triangle ABC is similar to triangle DEF. Triangle DEF is similar to triangle GHI. Determine the missing values. Explain your thinking. The figures may not be drawn to scale.
2. Triangle CAT is similar to triangle DOG. Triangle CAT is dilated by a scale factor of 1.5 creating triangle DELI. Determine the missing side lengths. Show or explain your thinking.
3. On a sunny day, a 6-foot-tall person has a shadow with a length of 9 feet. At the same time, a nearby tree has a shadow with a length of 24 feet. What is the height of the tree?
A. 12 feet
B. 16 feet
C. 18 feet
D. 20 feet

SnapAndSolve AI · Accepted Answer

To find the missing values, use the property of similar triangles that corresponding sides are proportional. If triangle ABC is similar to DEF, and DEF is similar to GHI, then the ratios of corresponding sides are equal. Set up proportions to solve for the missing values.
Since triangle CAT is similar to triangle DOG, the corresponding sides are proportional. When CAT is dilated by a scale factor of 1.5 to form DELI, multiply each side of CAT by 1.5 to find the side lengths of DELI.
Using the property of similar triangles, the ratio of the height of the person to their shadow is equal to the ratio of the height of the tree to its shadow. Set up the proportion: 6/9 = x/24. Solving for x gives x = 16 feet. Therefore, the height of the tree is 16 feet.

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Triangle ABC is similar to triangle DEF. Triangle DEF is similar to triangle GHI. Determine the missing...

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