Calculating Altitudes and Medians in Similar Triangles Using Scale Factors
This guide provides a step-by-step procedure for finding altitudes and medians in similar triangles, specifically focusing on triangles ∆TPR and ∆XPZ. Using the scale factor method, we establish proportions between corresponding lengths. We explore guided practice examples where the altitude of triangle PS is found to be 15, and the median KM is calculated using the same principles. This method relies on the intrinsic relationship between corresponding elements of similar figures, ensuring accuracy in geometric calculations.
Calculating Altitudes and Medians in Similar Triangles Using Scale Factors
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Presentation Transcript
In the diagram, ∆TPR~∆XPZ. Find the length of the altitude PS. TR 12 3 XZ 16 4 6 + 6 = = = 8 + 8 EXAMPLE 5 Use a scale factor SOLUTION First, find the scale factor of ∆TPRto ∆XPZ.
= 3 PS 3 4 4 PY PS = 20 = PS 15 The length of the altitude PSis 15. EXAMPLE 5 Use a scale factor Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion. Write proportion. Substitute 20 for PY. Multiply each side by 20 and simplify. ANSWER
7. In the diagram, ∆JKL ~ ∆ EFG. Find the length of the median KM. for Example 5 GUIDED PRACTICE In the diagram, ABCDE ~ FGHJK.
48 + 48 = = = 40 + 40 JL 96 6 EG 80 5 for Example 5 GUIDED PRACTICE SOLUTION First find the scale factor of ∆ JKL to ∆ EFG. Because the ratio of the lengths of the median in similar triangles is equal to the scale factor, you can write the following proportion.
= KM KM = 6 6 35 HF 5 5 KM = 42 for Example 5 GUIDED PRACTICE SOLUTION Write proportion. Substitute 35 for HF. Multiply each side by 35 and simplify.
