Download 3-4 Parallel Lines and the Triangle Angle-Sum Theorem

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. If no
triangle can be drawn, write not possible and explain why.
a) acute scalene
a)
Isosceles right
b)
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
a)
b)
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.
Now substitute!
RT = RS
3x - 5 = x + 7
2x - 5 = 7
2x =12
x=6
RS = 6 + 7
RS = 13
ST = 6 -1
ST = 5
RT = 3(6) - 5
RT =13
Corollary: statement that follows directly from a theorem
Example 7: Solve for each variable.
Try these.