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Transcript
Bell Ringer GPA page Bell Ringer Answers: 1. 3/9/17 11-1 Angle and Line Relationships I can examine relationships between pairs of angles. I can examine relationships of angles formed by parallel lines and a transversal. REVIEW: Basic Definitions: Ray – a part of a line that starts at one endpoint and extends forever. Angle – is formed by two rays with a common endpoint – Vertex. Congruent – same shape and size. Degrees – units for angle measures. Types of Angles: 1. Right angle – measures exactly 90° 2. Acute angle – measures less than 90° 3. Obtuse angle – measures more than 90° and less than 180° 4. Straight angle – measures exactly 180° Naming Angles: Use an angle symbol with three capital letters. Vertex must be in the middle. PAIRS OF ANGLES 1. Vertical Angles 2. Adjacent Angles 3. Complementary Angles 4. Supplementary Angles a pair (two angles) of opposite congruent angles formed by intersecting lines. Two angles whose measures add to 90° A pair of angles that share a common ray (side) and a vertex. Two angles whose measures add to 180° LINES 1. Perpendicular lines – lines in a plane that intersect to form four right angles 2. Parallel lines – lines in a plane that do not intersect 3. Transversal line – a line that intersects two parallel lines SPECIAL ANGLE RELATIONSHIPS (nonadjacent angles) 1. Alternate Exterior Angles – angles that are on opposite sides of the transversal and outside the parallel lines 2. Alternate Interior Angles – angles that are on opposite sides of the transversal and inside the parallel lines 3. Corresponding Angles – angles that are in the same position on the parallel lines in relation to the transversal EXAMPLE 1. Name the angle in four ways EXAMPLE 2. Classify the pairs of angles shown. Then find the value of x in each figure. A) B) C) EXAMPLE 3. In the figure at the right, r ǁs and w is a transversal. If m ∠1 = 128°, find the measure of each angle. Explain your reasoning. EXAMPLE 4. If m ∠ABD = 164°, find m ∠ABC and m ∠CBD. Homework: GPA page 622 (10-32 all)