Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 16940 by Tinkutara last updated on 28/Jun/17

Six points A, B, C, D, E, and F are  placed on a square rigid, as shown.  How many triangles that are not  right-angled can be drawn by using 3  of these 6 points as vertices?

$$\mathrm{Six}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C},\:\mathrm{D},\:\mathrm{E},\:\mathrm{and}\:\mathrm{F}\:\mathrm{are} \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{square}\:\mathrm{rigid},\:\mathrm{as}\:\mathrm{shown}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{triangles}\:\mathrm{that}\:\mathrm{are}\:\boldsymbol{\mathrm{not}} \\ $$$$\mathrm{right}-\mathrm{angled}\:\mathrm{can}\:\mathrm{be}\:\mathrm{drawn}\:\mathrm{by}\:\mathrm{using}\:\mathrm{3} \\ $$$$\mathrm{of}\:\mathrm{these}\:\mathrm{6}\:\mathrm{points}\:\mathrm{as}\:\mathrm{vertices}? \\ $$

Commented by Tinkutara last updated on 28/Jun/17

Answered by ajfour last updated on 28/Jun/17

 i could see only 4 such triangles.

$$\:\mathrm{i}\:\mathrm{could}\:\mathrm{see}\:\mathrm{only}\:\mathrm{4}\:\mathrm{such}\:\mathrm{triangles}. \\ $$

Commented by Tinkutara last updated on 28/Jun/17

Can you explain?

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}? \\ $$

Commented by ajfour last updated on 28/Jun/17

△DEC, △AEF, △ABF, △BCD .

$$\bigtriangleup\mathrm{DEC},\:\bigtriangleup\mathrm{AEF},\:\bigtriangleup\mathrm{ABF},\:\bigtriangleup\mathrm{BCD}\:. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com