Unit 5: Triangles & Polygons

Scalene

No congruent sides + no congruent angles

Isosceles

At least 2 congruent sides+ 2 or 3 congruent angles

Equilateral

3 congruent sides + 3 congruent angles

Acute

3 acute angles + each less than 90’

Right

1 right angle + 1 angle equals 90’

Obtuse

1 obtuse angle + 1 angle greater than 90’

Equiangular

3 congruent angles + 3 angles, each all measures 60’

Triangle Sum Theorm

The sum of the three interior angles in any triangle is 180 degrees

Vertex

A point at which two sides of a polygon intersect

Triangle inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Side-angle inequality theorem

In any triangle, the largest angle is opposite the longest side & the smallest angle is opposite the shortest side

Triangle exterior angle theorem

The exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles

Range of the 3rd side of a triangle

Subtract the given two sides (minimum) + add the given two side (maximum). The 3rd side is between the minimum & maximum. (MIN < X < MAX)

Ixl.F.2: TRIANGLE SUM THEOREM

m<1+m<2+m<3=180

If it's a missing number it's a

X

If it has a different letter after the number (9p) or (7c-48) or (2h+29)

It's an X

F.3. Exterior Angle Theorem

M<1+M<2=M<EXT

Example

109+31 =140 | x+17 +4x-36=x+48

Looking for angles: Angle 1= 60

(X+50+70=180)

Angle 2 : 33

(X+62+85=180)

Angle 3: 87

(X+33+60=180)

Whenever it’s vertical

It’s the number & congruent

Acute angles in a right triangle are

Complementary

Corollary= There can be ____ one __\ angled in a triangle

At most or right or obtuse

Triangle sum theorem

The sum of the interior angles in a triangle is 180

An exterior angle of a triangle (or any polygon) is

An angle that’s forms a linear pairs with an interior angles,?

They are the angles outside the polygon

Formed by extending a side of the triangle(or polygon) into a ray.

A is an

Interior angles

C is an

Exterior angles

The remote interior angles of a triangle (or any polygon are the two interior angles that are “far away from” a given exterior angle.

They are the angles that do not form a linear pair with a given exterior angle angle

Remote interior angled are

A & B

Exterior angles are

long line that hangs outside the story (C)

The memeasure of the exterior angles of a triangle is ______ of the memsures of _____.

Equal to the sum & the remote interior angles

M<ACD = m<A + m<B (3X-22=x+80)

M<A = 51