How to Prove two triangles are Similar ,they are congruent?

 

in Geometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

If two triangles are similar all their dimensions are in the same ratio. The area of a triangle is half the base times the height. If the ratio of the corresponding sides is R, and the height and base of one triangle are h and b, then the height and base of the other will be Rh and Rb and its area is (1/2)R^2hb, while the other triangle's area is (1/2)hb. If these areas are equal, R^2hb=hb, so R=1 or -1, which means that the sides of one triangle are equal in length to the corresponding sides in the other, and, by definition of similarity, the corresponding angles are equal. Therefore, the triangles are congruent. The triangles can be reflections of one another.

by Top Rated User (720k points)

Related questions

1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,525 questions
89,487 answers
1,999 comments
11,242 users