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7-1 Pairs of Angles

Video Tutor Help Word problem: find the missing angle Finding the measure of an angleFinding the measure of an angle (7-1) Vertical Angles Adjacent Angles Supplementary and Complementary Angles 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

7-1 Note Taking Guide 7-1 Practice 7-1 Guided Problem Solving 7-1 Worksheets

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

7-1 Step-by-Step Examples Additional Lesson Examples

Problem of the Day 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 Classify the angle using all names that apply. is less than Answer: So, is an acute angle. Classify Angles and Angle Pairs

Example 1-1b Classify the angle using all names that apply. Answer: right

Example 1-2a Classify the angle pair using all names that apply. are adjacent angles since they have the same vertex, share a common side, and do not overlap. Together they form a straight angle measuring Answer: are adjacent angles and supplementary angles. Classify Angles and Angle Pairs

Example 1-2b Classify the angle pair using all names that apply. Answer: adjacent, complementary

Example 1-3a The two angles below are supplementary. Find the value of x. Answer: 25 Subtract 155 from each side. Definition of supplementary angles Simplify. Find a Missing Angle Measure

Example 1-3b The two angles below are complementary. Find the value of x. Answer: 35

Pairs of Angles Find the measure of the supplement of  IGJ. LESSON 7-1 x° + m IGJ = 180° The sum of the measures of supplementary angles is 180º. x° + 145° – 145° = 180° – 145° Subtract 145º from each side. x° = 35° Simplify. The measure of the supplement of m IGJ is 35º. Additional Examples Substitute 145º for m DEF. x° + 145° = 180°

The adjacent angles are HGK and KGJ; KGJ and JGI; JGI and IGH; IGH and HGK. The vertical angles are JGI and HGK; HGI and KGJ. Pairs of Angles LESSON 7-1 Name a pair of adjacent angles and a pair of vertical angles in the figure. Find m HGK. Since vertical angles are congruent, m HGK = m JGI = 145°. Additional Examples

Pairs of Angles In this figure, if m DKH = 73°, find the measures of GKJ and JKF. LESSON 7-1 m DKE + 90°= 180° DKE and FKE are supplementary. m DKE= 90° Subtract 90º from each side. Additional Examples

Pairs of Angles (continued) LESSON 7-1 m KHE + 73° = 90° KHE and DKH are complementary. m KHE = 17° Subtract 73º from each side. GKJ and KHE are vertical angles. m GKJ = m KHE = 17° JKF and DKH are vertical angles. m JKF = m DKH = 73° So, the measure of GKJ is 17° is and the measure of JKF is 73°. Additional Examples