Question

A(n) _____ is a statement whose proof can be deduced directly from a previous theorem. auxiliary line remote interior angle corollary triangle 5) A triangle in which one of its interior angles is an obtuse angle is a(n) _____ triangle. equiangular right obtuse acute 6) A triangle with at least two congruent sides is a(n) _____ triangle. right auxiliary isosceles equiangular

Answer 1

The words in order are:

• corollary
• obtuse
• isosceles

Explanation:

A corollary is a quick conclusion of a theorem. The proof of a corollary is rather short, compared to the proofs of theorems and other propositions. For example, if you consider the theorem "the area of a circle of radius r is πr²" then an inmediate corollary is "the area of a semicircle of radius r is πr²/2".

Triangles can be classified according to their interior angles. The three types of triangles are acute, right and obtuse. Obtuse triangles are those that have an inner obtuse (>90°) angle. Right triangles have an inner right (=90°) angle, and acute triangles have 3 acute (<90°) inner angles.

Similarly, triangles can be classified according to their sides, as equilateral, isosceles and scalene. Equilateral triangles have all their 3 congruent sides, isosceles triangles have at least 2 congruent sides, and scalene triangles have no congruent sides.