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How can you determine the length of a missing side in similar triangles?
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Set up a proportion based on the corresponding sides and solve for the unknown using cross multiplication.
Given AB = 8, BC = 6, DE = 12. If these triangles are similar, what proportion would you set up to find EF?
You would set up the proportion 8/12 = 6/EF.
What is a crucial initial step in solving for missing sides using similar triangles?
Identifying which angles and sides correspond between the two triangles is crucial.
Given triangles ABC and DEC, with AB = 8, AC = 5, BC = 7, and DE = 12, find the value of DC.
DC = 10.5 using the proportion 8/12 = 7/x and solving 8x = 7*12.
Given AB = 8, AC = 5, BC = 7, DC = x, and DE = 12, what proportion do you set up?
Set up the proportion 8/12 = 7/x.
If AB = 18, BC = 24, DE = 30, and angle A ≈ angle F, set up the proportion to find EF.
EF = 22.5 using the proportion 24/30 = 18/x and solving 24x = 18*30.
How do you start solving for multiple missing sides in similar triangles?
Set up proportions for each pair of corresponding sides and solve each equation separately.
Explain how to find the missing side y in the triangles where BC = 24, DE = 30, and DF = 40.
Set up the proportion 24/30 = y/40, cross multiply 30y = 24*40, and solve for y to find y = 32.
What is the relationship between corresponding sides in similar triangles?
Corresponding sides are in proportion.
Given AB = 15, BC = 9, EF = x, and DF = x + 10, how do you solve for x?
Set up the proportion 15/(x+10) = 9/x, then cross multiply to get 15x = 9(x + 10), and solve for x.
What method can simplify solving the equation after cross multiplication?
Breaking down coefficients to cancel out common factors simplifies solving the equation.
Why is cross multiplication useful in solving proportions in similar triangles?
Cross multiplication turns the proportion into a simple equation that can be solved for the unknown value.
Given triangle ABC and DEF, with AB = 8, BC = 6, DE = 12, and EF = x. What is the value of EF?
EF = 9
In a set of similar triangles with AB = 18, BC = 24, DE = 30, what proportion helps to find EF?
The proportion 24/30 = 18/EF helps to find EF.
Explain the steps to find the value of EF in the problem where AB = 15, BC = 9, EF = x, DF = x + 10.
Set up the proportion 15/(x+10) = 9/x, cross multiply to get 15x = 9(x + 10), and solve for x to find EF = 15.
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