7.2 Exterior Angle Theorem. You will learn to identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem. 1)

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Presentation transcript:

7.2 Exterior Angle Theorem

You will learn to identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem. 1) Interior angle 2) Exterior angle 3) Remote interior angle

P QR In the triangle below, recall that  1,  2, and  3 are _______ angles of ΔPQR. interior Angle 4 is called an _______ angle of ΔPQR. exterior An exterior angle of a triangle is an angle that forms a _________ with one of the angles of the triangle. linear pair In ΔPQR,  4 is an exterior angle at R because it forms a linear pair with  3. ____________________ of a triangle are the two angles that do not form a linear pair with the exterior angle. Remote interior angles In ΔPQR,  1, and  2 are the remote interior angles with respect to  4.

In the figure below,  2 and  3 are remote interior angles with respect to what angle? 55

Theorem 7 – 3 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to sum of the measures of its ___________________. remote interior angles X ZY m  4 =m  1 + m  2

Theorem 7 – 4 Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measures of either of its two ____________________. remote interior angles X ZY m  4 >m1m1 m2m2

 1 and  3 74° 13 2 Name two angles in the triangle below that have measures less than 74°. Theorem 7 – 5 If a triangle has one right angle, then the other two angles must be _____. acute

The feather–shaped leaf is called a pinnatifid. In the figure, does x = y? Explain. x = y ? __ + 81 = ° 109 = 110 No! x does not equal y