Two triangles are on the same base and between the same parallels. Prove that the sides or sides produced intercept equal segments on any straight line parallel to the base. Let ABC, DBC be the triangles. Draw GEHF parallel to BC meeting AB, AC, DB, DC produced in E, F, G, H respectively. EF will be equal to GH. CONSTRUCTION : Through F draw FLK || AB; through G draw GNM || CD. Produce BC to L, N and AD to M, K. Join BF, GC A B G E H

Two triangles are on the same base and between the same parallels. Prove that the sides or sides produced intercept equal segments on any straight line parallel to the base. Let ABC, DBC be the triangles. Draw GEHF parallel to BC meeting AB, AC, DB, DC produced in E, F, G, H respectively. EF will be equal to GH. CONSTRUCTION : Through F draw FLK || AB; through G draw GNM || CD. Produce BC to L, N and AD to M, K. Join BF, GC A B G E H

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

See similar textbooks

Similar questions

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.
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(,_).
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.
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
If possible, draw an equilateral and concave: a triangle c pentagon
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
Is it possible to draw a triangle whose sides measure a. 8, 9, and 10? b. 8, 9, and 17? c. 8, 9, and 18?
Determine whether ABC, with vertices A0,0,0, B1,2,4, and C0,0,8, is an isosceles triangle.