Q. 74.3( 27 Votes )

Suppose a triangle is equilateral. Prove that it is equiangular.

Answer :

Capture.JPG


Δ ABC is an equilateral triangle


Let AD be the perpendicular from A on BC


In Δ ABD and Δ ACD


AB = AC (ΔABC is equilateral)


ADB = ADC (AD is a perpendicular)


AD = AD (Common side)


So Δ ABD and Δ ACD are congruent to each other by S.A.S. axiom of congruency


ABD = ACD (Corresponding Parts of Congruent Triangles)


BAD = CAD (Corresponding Parts of Congruent Triangles)


Since the triangle is equilateral and ABD = ACD, so


ABD = ACD = BAC


Hence the triangle is equiangular


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
NCERT | Standard Form of NumbersNCERT | Standard Form of NumbersNCERT | Standard Form of Numbers41 mins
Champ Quiz | Spelling of important wordsChamp Quiz | Spelling of important wordsChamp Quiz | Spelling of important words47 mins
Metals of SurprisesMetals of SurprisesMetals of Surprises38 mins
Quiz on Mystery of OnionQuiz on Mystery of OnionQuiz on Mystery of Onion30 mins
Out-of-the-box Concepts of Metals and Non-metalsOut-of-the-box Concepts of Metals and Non-metalsOut-of-the-box Concepts of Metals and Non-metals28 mins
Lets Learn Chemical EffectsLets Learn Chemical EffectsLets Learn Chemical Effects30 mins
Quiz | Effects of Electric CurrentQuiz | Effects of Electric CurrentQuiz | Effects of Electric Current23 mins
Champ Quiz | Revolt of 1857Champ Quiz | Revolt of 1857Champ Quiz | Revolt of 185749 mins
Benefits of Physical ActivityBenefits of Physical ActivityBenefits of Physical Activity36 mins
Foundation | Principle of CountingFoundation | Principle of CountingFoundation | Principle of Counting45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :