Lesson 12.3 The Pythagorean TheoremComplete the statement for the Pythagorean Theorem: a² + b² = c².27. a and b are the lengths of theof the right triangle.A) midsegmentB) medianC) hypotenuseD) legs28. c is the length of theof the right triangle.A) midsegmentB) medianC) hypotenuseD) legs

We will use statement of Pythagoras theorem

Answered: The Pythagorean Theorem tatement for…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.CR: Review Exercises

Problem 42CR

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Given: D is the midpoint of AC ACBC CD=2x+5 BC=x+28 Find: AC
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
Classify as true or false: a If the vertex angles of two isosceles triangles are congruent, the triangles are similar. b Any two equilateral triangles are similar.
Using as few variables as possible, state the coordinates of each point if DEF is isosceles with DEF is an isosceles triangle with D(,_),E(,_),F(,_).
Square RSTV has diagonals RT and SV not shown. If the diagonals are drawn, how will their lengths compare? Do the diagonals of a square appear to be perpendicular?
Determine the type of triangle represented if the lengths of its sides are: a a=1.5, b= 2 and c = 2.5 b a= 20, b= 21 and c = 29 c a=10, b= 12, and c =16 d a= 5, b= 7 and c = 9
a To locate the orthocenter, is it necessary to construct all three altitude of a right triangle? b What point is the orthocenter of any right triangle?
For a given triangle such as ABC, what word describes the point of concurrency for athe three perpendicular bisectors of sides? _____________ bthe three altitudes? ____________________
Is it possible to draw a triangle whose angles measure a. 100, 100, and 60? b. 45, 45, and 90?
Determine whether ABC, with vertices A0,0,0, B1,2,4, and C0,0,8, is an isosceles triangle.
In ABC, M is the midpoint of AB and N is the midpoint if AC. a How are the line segments MNandBC related? b Use an equation to state how the lengths MN and BC are related.
Consider the square at the right, RSTV. It has four right angles and four sides of the same length. How are sides RS and ST related? How are sides RS and VT related?

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The Pythagorean Theorem tatement for the Pythagorean Theorem: a? + b² = c². the lengths of the of the right triangle. egment B) median C) hypotenuse D) legs th of the of the right triangle. egment B) median C) hypotenuse D) legs