Classifying Triangles 4.1

acute triangle

A triangle with 3 acute angles (less than 90°)

equilateral triangle

A triangle with three congruent sides

An equilateral triangle is an equiangular triangle (Never, Sometimes, Always)

Always

An equiangular triangle is an isosceles triangle. (Never, Sometimes, Always)

Always -An equiangular ∆ has 3 congruent angles. And isosceles ∆ has at least 2 congruent sides AND at least 2 congruent opposite angles. Therefore an equiangular ∆ is also an isosceles ∆, but an isosceles ∆ is NOT always an equiangular ∆.

A right triangle is an obtuse triangle (Never, Sometimes, Always)

Never - A right triangle has one right angle (=90°), therefore the sum of the other 2 angles = 90° since the sum of the interior angle =180° always

An isosceles triangle is an equilateral triangle. (Never, Sometimes, Always)

Sometimes - An isosceles ∆ has at least 2 congruent sides AND at least 2 congruent angles. Therefore an isosceles ∆ may be equiangular ∆, but is NOT always an equiangular ∆.

A scalene triangle is an obtuse triangle (Never, Sometimes, Always)

Sometimes -A scalene ∆ may also be an acute ∆

An acute triangle is a scalene triangle (Never, Sometimes, Always)

Sometimes -an acute triangle may also be equilateral

equiangular triangle

a triangle in which all three angles have the same measure (60°)

isosceles triangle

a triangle with at least two congruent sides (could be 3 equal sides, but not always)

scalene triangle

a triangle with no congruent sides

obtuse triangle

has 1 obtuse angle (greater than 90°)

right triangle

has one right angle and two angles that are complementary (=90°)

Parts of a right triangle

hypotenuse - opposite right angle legs - other sides

An isoscles ∆ has two congruent legs. Leg a of an isosceles ∆ is equal to 4x-1.3 and leg b is equal to x +3.2. What is x? What is the length of leg a and leg b? Show algebraic proof.

leg a: 4x - 1.3, leg b: x +3.2 Given 4x-1.3=x+3.2 Definition of Isosc. ∆ 4x-1.3+1.3= x+ 3.2+1.3 Add'n Prop. 4x-x= x-x +4.5 Subtraction Property x= 4.5 leg a: (4)(4.5)-1.3 = 16.7 Substitution Prop leg b: 4.5+3.2=7.7 Substitution Prop.

Parts of an Isosceles Triangle

legs - the congruent sides of the ∆ base - the other side of the ∆

vertex

point where two lines, line segments, or rays meet

If you know one leg of an isosceles triangle, you can find the length of the other leg by _____

setting the sides equal to each other in an equation

adjacent sides of a triangle

sides that share a common vertex