2. Students will be able to:
◦ Find measures of angles of triangles
◦ Use parallel lines to prove theorems about triangles
◦ Define and apply the triangle sum and triangle
exterior angle theorems
3. The sum of the angles of a triangle is 180
degrees
4. List some things you know about triangles
The sum of the angles add to be 180
There are obtuse, acute, and right triangles
There are scalene, equilateral, and isosceles
triangles
In a right triangle, the two acute angles add
to be 90 degrees
5. Through a point not on a line, there is one
and only one line parallel to the given line.
6. Sometimes when proving things we need to
add lines to the diagram.
Auxiliary Line: a line you add to a diagram to
help explain relationships in proofs.
In the picture below the red line was added to
help with the following proof.
7. Statements Reasons
1. ΔABC 1. Given
2. Draw line PR through B, 2. Parallel Postulate
parallel to AC
3.<1, <2, <3 are Suppl 3. Def. of Linear Pairs
4. Def. of Suppl. <s
4.<1 + <2 + <3 = 180
5. Alt. Interior Angles
5. <1 ≅<A, <3 ≅<C
6. m<1 = m<A, m<3 = m<C 6. Def. of Congruence
7. m<A + m<2 + m<C = 180 7. Substitution
8. The sum of the measures of the angles of a
triangle is 180.
If you know the measures of two angles of a
triangle, you can use this theorem to find the
third measure.
9. What are the values of x, y, and z?
X = 102
Y = 78
Z = 66
10. Exterior Angle of a Polygon
◦ An angle formed by a side and an extension of an
adjacent side.
Remote Interior Angles
◦ The two nonadjacent interior angles to the exterior
angle
Below <1 is the exterior angle, <2 and <3 are
the remote interior angles
11. The measure of the exterior angle equals the
sum of the two remote interior angles.
mExterior Angle = Remote Int. + Remote Int
m<1 = m<2 + m<3
