7-2 Angles and Parallel Lines

Video Tutor Help Word problem: find the missing angle Relating angles and parallel linesRelating angles and parallel lines (7-2) Angles and Parallel Lines Transversal Corresponding Angles Alternate Interior Angles Identifying Parallel Lines Khan Academy

Video Tutor Help Finding the measure of an angle Exploring angles and transversals Identifying congruent triangles Using proportion to find unknown length in similar figures Finding the angle measures of a polygon Finding the angle measures of a regular polygon

7-2 Note Taking Guide 7-2 Practice 7-2 Guided Problem Solving 7-2 Worksheets

Chapter 7 Vocabulary (Electronic) Flash Cards Vocabulary Practice Vocabulary Graphic Organizer

7-2 Step-by-Step Examples Additional Lesson Examples

7-2 Problem of the Day 7-2 Lesson Quiz Lesson Readiness

Angles Acute angles: have measures less than Right angles: have measures equal to Obtuse angles: have measures between 90 0 and Straight angles: have measures equal to

Vertical Angles Vertical angles: are opposite angles formed by intersecting lines. Vertical angles are congruent ∠1 and ∠2 are vertical angles. ∠1 ≌ ∠2

Adjacent Angles Adjacent angles: have the same vertex, share a common side, and do not overlap. A B C ∠1 and ∠2 are adjacent angles. m∠ABC = m∠1 + m∠2 1 2

Complementary Angles The sum of the measures of complementary angles is 90 o. A B C D 40 o 50 o ∠ ABD and ∠ DBC are complementary angles. m ∠ ABD + m ∠ DBC = 90 o

Supplementary Angles The sum of the measures of supplementary angles is 180 o. 125 o 55 o ∠ C and ∠ D are supplementary angles. m ∠ C + m ∠ D = 180 o. C D

Lines Lines that intersect at right angles are called perpendicular lines. Red arrowheads indicate that lines p and q are parallel. p q p II q A red right angle symbol indicates that lines m and n are perpendicular, m n m n Two lines in a plane that never intersect or cross are called parallel lines.

Transversal A line that intersects two or more other lines is called transversal. When a transversal intersects two lines, eight angles are formed that have special names. If the two lines cut by a transversal are parallel, then these special pairs of angles are congruent transversal

Reading Math Interior and exterior angles: when two lines are cut by a transversal, the interior angles lie inside the two lines, the exterior angles lie outside the two lines.

Parallel Lines Alternate interior angles, those on opposite sides of the transversal and inside the other two lines, are congruent Example: ∠ 2 ≌ ∠ 8 Alternate exterior angles, those on opposite sides of the transversal and outside the other two lines, are congruent. Example: ∠ 4 ≌ ∠ 6 Corresponding angles, those in the same position on the two lines in relation to the transversal, are congruent. Example: ∠ 3 ≌ ∠ 7

Example 1-1a In the figure, m || n and t is a transversal. If find m  2 and m  8. Sinceare alternate exterior angles, they are congruent. So,. Sinceare corresponding angles, they are congruent. So,. Answer: Find Measures of Angles

In the figure, m || n and t is a transversal. If find m  5 and m  1. Example 1-1b Answer:

Example 1-2a Read the Test Item Since are complementary,. Multiple-Choice Test Item If and  D and  E are complementary, what is m  E ? A 53° B 37° C 127° D 7° Find a Missing Angle Measure

Example 1-2a Solve the Test Item Complementary angles Replace with 53°. Subtract 53 from each side. Answer: The answer is B.

Example 1-2b Answer: A Multiple-Choice Test Item Ifand  G and  H are supplementary, what is m  h ? A 76° B 104° C 83° D 14°

Example 1-3a Angles PQR and STU are supplementary. If and, find the measure of each angle. Step 1 Find the value of x. Supplementary angles Substitution Combine like terms. Add 80 to each side. Divide each side by 2. Find Measures of Angles

Example 1-3a Step 2Replace x with 130 to find the measure of each angle. Answer:

Example 1-4a Transportation A road crosses railroad tracks at an angle as shown. Iffind m  6 and m  5. Sinceare corresponding angles, they are congruent. Answer: Sinceare supplementary angles, the sum of their measures is 180°. 180 – 131 = 49 Apply Angle Relationships

1 and 3, 2 and 4, 5 and 7, 6 and 8 are pairs of corresponding angles. 2 and 7, 3 and 6, are pairs of alternate interior angles. Angles and Parallel Lines LESSON 7-2 Identify each pair of corresponding angles and each pair of alternate interior angles. Additional Examples

Angles and Parallel Lines LESSON 7-2 If p is parallel to q, and m 3 = 56º, find m 6. m 6 = 56° m 6 = m 3 = 56° Alternate interior angles are congruent. Additional Examples

p || q because 5 and 7 are congruent alternate interior angles. s || t because 6 and 7 are congruent corresponding angles. Angles and Parallel Lines In the diagram below, m 5 = m 6 = and m 7 = 80º. Explain why p and q are parallel and why s and t are parallel. LESSON 7-2 Additional Examples