Unit 2: Properties of Angles and Triangles

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Presentation transcript:

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 The interior angles on the same side of the transversal are supplementary (add to 180°)

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

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

Example 1 (p.87)

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

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

Proof (p.88)

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

Example Determine the value of x.

Example Determine all the unknown angles.

Need to Know In any triangle, the sum of the measures of the interior angles is proven to be 180°. 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.

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

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