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Unit 2: Properties of Angles and Triangles

Unit 2: Properties of Angles and Triangles. Recall. When a transversal intersects two parallel lines, The corresponding angles are equal The alternate interior angles are equal The alternate exterior angles are equal

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Unit 2: Properties of Angles and Triangles

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  1. Unit 2: Properties of Angles and Triangles

  2. Recall • When a transversal intersects two parallel lines, • The corresponding angles are equal • The alternate interior angles are equal • The alternate exterior angles are equal • The interior angles on the same side of the transversal are supplementary (add to 180°)

  3. 2.3 Angle Properties in Triangles • What would be the sum of all the interior angles of a triangle?

  4. Exterior angle: the angle that is formed by a side of a polygon and the extension of an adjacent side

  5. Example 1 (p.87)

  6. Non-adjacent interior angles: The two angles of a triangle that do not have the same vertex as an exterior angle

  7. Example 2 (p.88) • Determine the relationship between an exterior angle of a triangle and its non-adjacent interior angles

  8. Proof (p.88)

  9. Example 3 (p.88) • Determine the measures of <NMO, <MNO and <QMO

  10. Example • Determine the value of x.

  11. Example • Determine all the unknown angles.

  12. Need to Know The measure of any exterior angle of a triangle is proven to be equal to the sum of the measures of the two non-adjacent interior angles. • In any triangle, the sum of the measures of the interior angles is proven to be 180°.

  13. Info for homework Then what can you say about the angles opposite of two equal sides in a triangle? (isosceles triangle) • What can you say about the angles of a triangle that have all equal sides? (equilateral triangle)

  14. Homework • P. 90-93 • # 3,5, 7, 9, 11,13, 14, 15,

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