Math Problem Statement
Solution
The two triangles and are given as similar (). From the properties of similar triangles, we know that corresponding sides are proportional.
The corresponding sides of the triangles are:
- corresponds to
- corresponds to
- corresponds to
We can now set up ratios of corresponding sides to solve for and .
Step 1: Set up the proportion for side and
Given:
Using the ratio , we can use corresponding sides: Simplify to : Cross-multiply: Simplify: Solve for :
Step 2: Set up the proportion for side and
Now, to solve for , we use the ratio .
Given:
Use the ratio: Simplify : Since the ratio holds, the corresponding sides are proportional.
For side , we know that:
Final Answers:
Would you like further details or explanations?
Here are some related questions:
- What is the relationship between the angles in similar triangles?
- How do you calculate the area of similar triangles if one side length is known?
- How does the ratio of corresponding sides affect the perimeter of similar triangles?
- What happens to the ratio of the areas when two triangles are similar?
- Can two triangles be similar if their corresponding angles are not equal?
Tip: In similar triangles, the ratio of any two corresponding sides is always constant.
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Math Problem Analysis
Mathematical Concepts
Similar Triangles
Proportionality
Algebra
Formulas
Ratio of corresponding sides: (AC / DF) = (AB / DE)
Cross multiplication for solving proportions
Theorems
Theorem of Similar Triangles
Proportionality of corresponding sides
Suitable Grade Level
Grades 8-10