6. Let AABC be a triangle and let D, E, and F be the midpoints of the sides BC, AC, and AB, respectively. (a) Prove that AEDC is not similar to AABC. . (b) Prove that the congruences AF = ED, AE = FD, and BD = EF cannot all hold. (c) Compare the results above with the Euclidean theorems about medial triangles in Exercise 5.6.2.

6. Let AABC be a triangle and let D, E, and F be the midpoints of the sides BC, AC, and AB, respectively. (a) Prove that AEDC is not similar to AABC. . (b) Prove that the congruences AF = ED, AE = FD, and BD = EF cannot all hold. (c) Compare the results above with the Euclidean theorems about medial triangles in Exercise 5.6.2.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 34E: Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b,...

See similar textbooks

Similar questions

a Does the similarity relationship have a reflexive property for triangles and polygons in general? b Is there a symmetric property for the similarity of triangles and polygons? c Is there a transitive property for the similarity of triangles and polygons?
Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then _. b If ab and bc, then _.
Consider noncoplanar points A, B, C, and D. Using three points at a time such as A, B, and C, how many planes are determined by these points?
Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle. Exercises 34. 35
Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.
Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.
a Are any two regular pentagons similar? b Are any two equiangular pentagons similar?
Which part hypothesis or conclusion of a theorem determines the a Drawing? b Given? c Prove?