Post on 30-Dec-2015
transcript
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 .
Ex.5: Find the measure of in the diagram shown.
m JKM
1
• 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
Ex.8: Find the measure of each interior angle of ∆ABC, where
, 2 ,& 3 .o o om A x m B x m C x
.m G
Ex.9: Find the measures of the acute angles of the right triangle in the diagram shown.