Section 3-4 Angles of Triangles What is a triangle?

Triangles Definition A figure where three segments join at three points Parts Vertex Sides

Classifying or Describing Triangles Sometimes by the number of congruent SIDES Sometimes by the its ANGLES

Classifying by Sides Scalene triangle No congruent sides Isosceles triangle At least two congruent sides Equilateral triangle All sides congruent

Classifying by Angles Acute Obtuse Right Equiangular Three acute angles One obtuse angle One right angle All congruent angles

Side Note Often diagrams needed for proofs are lacking elements. If this is the case an AUXILIARY LINE (or ray or segment) can be drawn to help with the proof. AUXILIARY LINES are denoted using a dotted/dashed line.

Theorem 3-11 The sum of the measures of the angles of a triangle is 180. Prove using the diagram on the board.

Practice Find the missing angle then state whether the triangles are acute, obtuse or right 1. 55, , , , , Acute 2. Right 3. Acute 4. Obtuse 5. Right

Review: What can be used as reasons in a proof? Properties/Properties Given Theorems we already proved And …

A Corollary - a statement easily proved after a theorem is given

Now that we have theorem 3-11 What can be said about equiangular triangles?

Corollary 2 Each angle of an equiangular triangle is 60°. Draw me a equiangular triangle.

Using theorem 3-11 Can a triangle have two angles greater than or equal to 90°? Draw me a triangle with two obtuse angles? Can it be done? What about with two right anlges?

Corollary 3 In a triangle, there can be at most one right or obtuse angle.

Using theorem 3-11 In a right triangle what can be said about the two other angles? Draw me a right triangle and make a conclusion about the other two angles.

Corollary 4 The acute angles of a right triangle are complementary.

Using theorem 3-11 If triangle 1 has angles 30, 70 and y and triangle 2 has angles x, 70 and 30 then what do we know about x and y?

Corollary 1 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

Finding the missing angle measurements of triangles. Using the transparency find the measure of angle A.

Theorem 3-12 The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.

Now let’s look at the CE on p.96 Homework:Written exercises pg 97 #1-16