GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM

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Geometry 3-4: Parallel Lines and the Triangle Angle-Sum Theorem

Geometry 3-4: Parallel Lines and the Triangle Angle-Sum Theorem


Objective 1: To classify triangles and find the measure of their angles.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM

Theorem 3-12: Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is _________.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM

Example 1: Applying the Triangle Angle –Sum Theorem

A) Find the values of x and y.

To find the value of x, use

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM

To find the value of y,






B) Find the value of z two different ways using the Triangle Angle-Sum Theorem.










In Chapter 1, you classified an angle by its _________________. You can also classify a triangle by its _______________ and _____________.



By Sides:

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM





_____________________ _____________________ ____________________

_____________________ _____________________ ____________________

By Angles:

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM






______________________ _____________________ __________________

______________________ _____________________ __________________



GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM




_____________________

_____________________



Example 2: Classifying a Triangle

A: Classify each triangle by its sides and its angles.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM




B: Draw and mark a triangle to fit each description. If no triangle can be drawn, write not possible and explain why.


a.) acute scalene b.) isosceles right c.) obtuse equiangular







Objective 2: To use exterior angles of triangles


An ________________________ of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its ___________________________________________________________.


GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM

Theorem 3-13: Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM



Example 3: Using the Exterior Angle Theorem to find each missing angle measure

A. B.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM



C. D. Explain how you can find the measure of GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM 1 in

Ex C without using the Exterior Angle Theorem.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM




E. Two angles of a triangle measure 45. Find the measure of an exterior angle at each vertex.

(Hint: draw a picture)






Example 4: The lounge chair has different settings that change the angles formed by its parts. Suppose GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM and GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM . Find GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM , the angle formed by the back and the arm rest.

GEOMETRY 34 PARALLEL LINES AND THE TRIANGLE ANGLESUM THEOREM



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Tags: lines, geometry, triangle, anglesum, theorem, parallel