Classification
*picture of an equilateral* What triangle is this?
an equilateral triangle
an angle formed by two sides of a triangle is known as what?
interior angle
What type of triangle has a right angle?
Right triangle
What theorem is this? The sum of the measures of the angles of a triangle is always 180
Triangle Sum Theorem
Classify triangle ABC. *picture of acute isoceles triangle*
acute isoceles triangle
*picture of an obtuse triangle* What triangle is this?
obtuse triangle
What is an angle outside a triangle formed by one side of the triangle and the extension of adjacent angle?
exterior angle
A triangle with 3 congruent sides and 3 congruent angles is known as...
An equilateral triangle
What theorem is this? A triangle is an isoceles triangle if and only if the base angles are congruent
isoseceles triangle theorem
Given triangle DEF, m<D=(2x+2), m<E=(2x+10), m<F=(16x+32). Draw what the triangle looks like.
*drawing of the triangle*
*picture of an isoceles acute* What triangle is this?
isoceles acute triangle
*picture of triangle labeled* What is <A and <B?
They are remote interior angles
*picture of a scalene triangle* What triangle is this?
Scalene triangle
What is the exterior angle theorem?
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles
Given triangle DEF, m<D=(2x+2), m<E=(2x+10), m<F=(16x+32). Solve for x.(Your answer should be a decimal)
x=6.8
triangle ABC sides are A=20 B=130 and C=30. What kind of triangle is this?
scalene obtuse triangle
*picture of triangle with lines* Which angles are interior angles?
<A, <B, and <C
*picture of an equilateral triangle* How do we know this is an equilateral triangle?
How can we determine a triangle is an isoceles triangle?
By using the isoceles triangle theorem and looking to see if the base angles are congruent
Given triangle DEF, m<D=(2x+2), m<E=(2x+10), m<F=(16x+32). Determine the measures of the angles.
D=15.6
E=23.6
F=140.8
*picture of acute isoceles triangle* How do you know this is a right isoceles triangle?
The base angles are equal and all the angles equal less then 90 degrees
*picture of labeled triangle* Which angle is an angle outside a triangle formed by one side of the triangle and the extension of an adjacent side? Give an example from the picture.
A exterior angle. Ex. <D
Classify this triangle. *picture of a scalene obtuse triangle*
Scalene Obtuse
*picture of exterior angle theorem example* How would you find the measures of these angles?
by using the exterior angle theorem to prove that the exterior angles are equal to the measure of its remote interior angles
In triangle GHI, <G is congruent to <I. GH=6x+20, HI=4x+40, GI=4x-5. Find the lengths of all 3 sides
GH=80
HI=80
GI=35