Transcript Chapter 4.1 Notes: Apply Triangle Sum Properties

Chapter 4.1 Notes: Apply
Triangle Sum Properties
Goal: You will classify triangles and find
measures of their angles.
• A triangle is a polygon with three sides.
• A triangle with vertices A, B, and C is called
“triangle ABC” or “∆ABC.”
Classifying Triangles by Sides
• A scalene triangle is a triangle with no congruent
sides.
• An isosceles triangle is a triangle with at least two
congruent sides.
• An equilateral triangle is a triangle with three
congruent sides.
Classifying Triangles by Angles
• An acute triangle is a triangle with three acute
angles.
• A right triangle is a triangle with one right angle.
• An obtuse triangle is a triangle with one obtuse
angle.
• An equiangular triangle is a triangle with three
congruent angles.
Ex.1: Classify the triangular shape of the support
beams in the diagram by its sides and by measuring
its angles.
Ex.2: Classify the triangle shown in the diagram by its
sides and angles.
Ex.3: Classify the triangle by its sides and angles.
Angles
• When the sides of a polygon are extended, other
angles are formed.
• The original angles are the interior angles.
• The angles that form linear pairs with the interior
angles are the exterior angles.
• Theorem 4.1 Triangle Sum Theorem:
The sum of the measures of the interior angles of a
triangle is 180o.
• Theorem 4.2 Exterior Angle Theorem:
The measure of an exterior angle of a triangle is
equal to the sum of the measures of the two
nonadjacent interior angles.
Ex.4: Find mJKM.
Ex.5: Find the measure of 1 in the diagram shown.
• A corollary to a theorem is a statement that can be
proved easily using the theorem.
• Corollary to the Triangle Sum Theorem:
The acute angles of a right triangle are
complementary.
Ex.6: The tiled staircase shown forms a right triangle.
The measure of one acute angle in the triangle is
twice the measure of the other. Find the measure of
each acute angle.
Ex.7: Find mG.
Ex.8: Find the measure of each interior angle of
∆ABC, where
mA  x , mB  2 x ,&mC  3x .
o
o
o
Ex.9: Find the measures of the acute angles of the
right triangle in the diagram shown.