EXTERIOR ANGLE THEOREM - South Hadley Public Schools · 72 no anim.notebook 3 Dec 156:26 PM 1 2 34...

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72 no anim.notebook 1 Dec 155:30 PM Section 72 EXTERIOR ANGLE THEOREM Dec 155:39 PM 1 2 3 4 5 6 7 8 9 10 11 12 A B C An exterior angle of a triangle is an angle that forms a linear pair with one of the interior angles of a triangle. Exterior Angles Each exterior angle has two remote interior angles associated with it. Remote interior angles of a triangle are the two interior angles that are away from an exterior angle.

Transcript of EXTERIOR ANGLE THEOREM - South Hadley Public Schools · 72 no anim.notebook 3 Dec 156:26 PM 1 2 34...

Page 1: EXTERIOR ANGLE THEOREM - South Hadley Public Schools · 72 no anim.notebook 3 Dec 156:26 PM 1 2 34 The Exterior Angle Theorem The measure of an exterior angle is equal to the sum

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Section 7­2

EXTERIORANGLE

THEOREM

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An exterior angle of a triangle is anangle that forms a linear pair with one of the interior angles of a triangle.

Exterior Angles

Each exterior angle has two remote interior angles associated with it. Remote interior angles of a triangle are the two interior angles that are away from an exterior angle.

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PQ

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Example 1

a.  Name the two remote interior angles     of ΔPQR with respect to

b.  Name the two remote interior angles     of ΔPQR with respect to

c.  Name the two remote interior angles     of ΔPQR with respect to

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R

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N1

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Use a straightedge to draw and label ΔRPN.  Extend side         through K to form theexterior angle 4. 

1.  Use a protractor to find 2.  Use a protractor to find

3.  Use a protractor to find 4.  Find

Make a conjecture about how the measure of an exterior angle relates to the measures of its two remote interior angles. 

K

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The Exterior Angle TheoremThe measure of an exterior angle is equal to thesum of the measures of its two remote interior angles.

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Example 2

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a.  If                    and                        what is

b.  What is           if                     and

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c.  If                                         and                   find the value of x.

Example 2 continued

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d.  If                                         and                  find the value of x.     Then find 

Example 2 continued

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The measure of an exterior angleis greater than the measures ofeither of its two remote interiorangles.

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If a triangle has one right angle, then the other two angles must be acute.

Two More Theorems


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