Presentation on theme: "What we do in life echoes in eternity.. 7.4 Similarity in Right Triangles LT: To find and use relationships of similar right triangles."— Presentation transcript:
What we do in life echoes in eternity.
7.4 Similarity in Right Triangles LT: To find and use relationships of similar right triangles.
Similarity in Right Triangles Theorem 7-3: The altitude to the hypotenuse of a right triangle divides the triangles into two triangles that are similar to the original triangle and to each other.
Geometric Mean Geometric Mean: The number x such that, where a, b, and x are positive numbers Find the geometric mean of 3 and 27. Review: How do we find the arithmetic mean of 3 and 27? Note: Find the geometric mean of 4 and 18. The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers.mathematicsmeanaverage
1.The geometric mean can give a meaningful "average" to compare two companies. 2.The use of a geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting. 3.The geometric mean applies only to positive numbers.   4.It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.human population Purpose of the Geometric Mean
Geometric Mean 5.2 in8.75in 6.75in Corollary to Theorem 7-3: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse
Similarity in Right Triangles Find the values of x and y in the following right triangle. 4 5 X Y Y X 4 + 5
You Try One!!! Find the values of x and y in the following right triangle.
You wasted $150,000 on an education you coulda got for $1.50 in late fees at the public library.
7.4 Similarity in Right Triangles HW (7.4) Pgs : #1-21, 34, 35, 50, 51
Proof of Corollary to Theorem 7-3 A C D B StatementsReasons Altitude of rt. Δ to hypotenuse divides into 2 ~ Δs
Real World Connection As Marla arrives at the lake from the parking lot, she reads a sign that says she is 320m from the dock. How far is Marla from the information center?
Kick it up a notch! Find the value of x in the following right triangle. x1 2x - 1