Find the lengths of the legs.
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What is the length of the diagonal?
A square has a diagonal of length 5 cm. What is the area of the square?
Priya is teaching her younger cousin to ride a bike. She wants to stay on roads that are not too steep and easy enough for a new bike rider. She has decided the roads must have an angle less than or equal to 7 degrees. A 7 degree angle in a right triangle has a \(3:25\) ratio for the legs. List the legs of 2 right triangles that would be safe for a new bike rider.
Clare and Han are discussing how to find the missing lengths. Clare says she is using similarity. Han says he is using the Pythagorean Theorem.
- Do you agree with either of them? Show or explain your reasoning.
- Find the missing sides.
In right triangle \(ABC\), angle \(C\) is a right angle, \(AB\) is 25 units long, and \(BC\) is 24 units long. What is the length of \(AC\)?
- Find the length of \(EF\).
- Find the measure of angle \(E\).
Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning.
- Isosceles triangles are similar.
- Equilateral triangles are similar.