MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
x
Institutions: Global | Authors |Cars | Courseware |Ekurhuleni Libraries | Joburg Libraries | Startups | Tools |Tshwane Libraries | Math Worksheets | Visual Statistics

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
316 views
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio
in Mathematics by Diamond (62,244 points) | 316 views

1 Answer

0 like 0 dislike
Lets have △ABC with line DE∥BC

We have to prove that AD/DB=AE/EC

construct or draw  h1 from E perpendicular to AD, and h2 from D perpendicular to AE.

Draw BE and CD.

Area △ADE/Area △BDE =1/2AD.h1/[1/2DB.h1

                                          =AD/DB Area △ADE/Area △CED=1/2AE.h2/[1/2EC.h2]=AE/EC

but     Area △BDE=Area △CED (equal base and height)

hence Area △ADE/Area △BDE = Area △ADE/Area △CED

Therefore AD/DB = AE/EC

Repeating the same method, we can show that:

AD/AB = AE/AC and AB/BD = AC/CE
by Diamond (42,470 points)

Welcome to MathsGee Answers, a free online study network where students can ask, answer, and explore 24/7 for improved outcomes.



MathsGee Supporting City of Joburg

Enter your email address:

Registered Members Online
MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Interactive Courseware

ZeroEd Search Engine

Article Rewriter Tool

Word Counter Tool

Other Tools

STEM Gender Equality | ZOOM | Slack | eBook