3.4 & 4.5 Triangles

3-4 Parallel Lines and the Triangle Angle-Sum Theorem Objectives: 1) to classify triangles and find the measures of their angles 2) To use exterior angles of triangles

Watch the Video for the Proof of Triangle Angle-Sum Theorem

Example 1: Find the values of x, y, and z.

You try. Find the values of x, y, and z.

You can classify a triangle by its angles and sides.

Try these. Draw and mark a triangle to fit each description Try these. Draw and mark a triangle to fit each description. If no triangle can be drawn, write not possible and explain why. acute scalene Isosceles right Obtuse equiangular

Exterior angle of a polygon: angle formed by a side and an extension of an adjacent side Remote interior angles: the two nonadjacent interior angles

Proof of Triangle Exterior Angle Theorem

Example 3: Find each missing angle.

Try this. Find the measure of angle 1. 125=90+m∠1 35=m∠1

Try this one too.

Example 4: Find the value of x.

4-5 Isosceles and Equilateral Triangles Objective: use and apply properties of isosceles triangles

What is an Isosceles Triangle? Isosceles triangle: A triangle with at least two congruent sides Legs: The congruent sides of an isosceles triangle Base: The “other” side not counting as the two congruent sides Vertex angle: The angle included by the two congruent sides Base angles: The Angles that include the Base

Example 5: Solve for Variable

c) d)

Try these.

Example 6: Apply Concepts Triangle RST is an isosceles triangle. R is the vertex angle, RS = x + 7, ST = x – 1, and RT = 3x – 5. Find x, RS, ST, and RT.

Corollary: statement that follows directly from a theorem

Example 7: Solve for each variable.

Try these.