Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 691.

## Sunday, November 20, 2011

### Problem 691: Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya

Labels:
20,
80 degrees,
angle,
congruence,
isosceles,
triangle

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This is far easy one!

ReplyDeleteAC=CB and AE perpendicular to DC, then ACED is a deltoid so <CDE=30.

x=50-30=20 and we are done here (:

http://img191.imageshack.us/img191/4097/problem691.png

ReplyDeleteSince triangle ABC is isosceles so (BAC)=(BCA)=80

And (DAE)=40 and (DCE)=30

Triangle DAE congruent to Tri. CAE ( case SAS)

So DE=EC and ( CDE)=(ECD)=30

In triangle DAF, x=180-80-80=20

Peter Tran

Sí pero yo creo que quisiste decir que AC = AD o no?

ReplyDeleteAC=AD, efectivamente. gracias @Markov

ReplyDelete<ADC is an exterior angle, then tr ADC is isosceles, so we have AD = AC, cause this triangles CAE and DAE are congruents by SAS.

ReplyDeleteThen ADF is 80 80 20 , therefore x=20

Greetings ^^

AE is easily seen to be the perpendicular bisector of DC hence Tr. DEC is isoceles and < CDE = 30 and so x= 20

ReplyDeleteCan anyone show that Tr. BEF is isoceles?

Sumith Peiris

Moratuwa

Sri Lanka

Using symmetry, <CEF and <DEB are 60 each. Since <BDE is 100 and <CEF is 100 by difference (180- 60-20). Therefore, TR DEB is congruent to Tr ECF (ASA). Since corr sides of cong Tr are equal, EF = EB making TR BEF isoceles.

Delete....and that BD = CF?

ReplyDelete...also that AE is perpendicular to BF?

ReplyDelete