Ch. 10 Geometry: Line and Angle Relationships

Vocabulary for angles: Acute angles: less than 90° Right angles: 90° Obtuse angles: more than 90° Straight angles: 180 °

Vocabulary for angles: Vertical angles: opposite angles form by intersecting lines. Vertical angles are congruent. So,∠1=∠2; ∠3 =∠4 Complementary angles: sum of angles is 90 ∠60° +∠30° =∠90° Supplementary angles: sum of angles is 180 ° So,∠120° +∠60° =∠180° 1 2 3 4 30° 60° 120 ° 60°

Line and Angle Relationships Can you tell their names? Acute Angle Vertical Angles Obtuse Angle Complementary angles 45° 45° ∠3 ∠1

Line and Angle Relationships Can you tell their names? Right angles Straight angles Supplementary angles 135° 45° 180°

Line and Angle Relationships This is a complementary angle. The sum of angles = 90°. So, x° + 35° = 90° x = 90° - 35° x = 55° 2. Find the missing angles Example 1: 35° x°

Line and Angle Relationships 2. Find the missing angles Example 2: This is a supplementary angle. The sum of angles = 180°. So, 45° + x° + 55° = 180° x = 180°- 55° - 45 ° x = 180° - 100 ° x = 80° 45° x° 55°

Line and Angle Relationships 2. Find the missing angles Example 3: They are a vertical angles. The opposite angles congruent to one another. So, x° = 75° y° = 105° Reason: vertical angles 105° 75° x° y°

Line and Angle Relationships 2. Find the missing angles Your turn: x° + 60° = 90° x = 90° - 60° x = 30° x° 60°

Line and Angle Relationships 2. Find the missing angles Your turn: x° = 120° y° = 60° Reason: vertical angles 60° 120° x° y°

Ch. 6-1 Line and Angle Relationships 2. Find the missing angles Your turn: This is a supplementary angle. The sum of angles = 180°. So, 80° + x° + 35° = 180° x = 180°- 80° - 35 ° x = 65° x° 80° 35°

Vocabulary for lines: Perpendicular Lines: Lines intercept at right angles. Symbol: e.g. m n Parallel Lines: Lines never intersect or cross. Symbol: II Transversal: A line that intersects 2 or more lines. Right angle symbol indicates the lines are perpendicular. The arrowheads indicate that two lines are parallel.

Vocabulary for lines: Alternate Interior Angles are congruent What happen when a transversal passes through two parallel lines? Alternate Interior Angles are congruent So, x°= y° 2. Alternate Exterior Angles are congruent So, a°= b° 3. Corresponding angles are congruent. So, s°= t ° x° y° a° b° s ° t °

Line and Angle Relationships 3. Find the angle measure Example 1 (2001 FCAT): Tyrone is building a picnic table to be used in a local park. An end view of the picnic table is shown below. Tyrone needs to know the measure of angle x. The top of the table will be parallel to the ground. One side of each leg will meet the ground at a 145° angle. What is the measure, in degrees, of angle x? A. 35 ° B. 45 ° C. 145 ° D. 180 ° 145° x° Angle x ° and angle 145 ° are alternate interior angles. They are congruent. So, x ° = 145 ° C is the answer

Line and Angle Relationships 1. Find ∠2 if ∠1 = 63° ∠2 and ∠1 are corresponding angles. Their angles are congruent. So, ∠2 = ∠1 = 63 °. 2. Find ∠3 if ∠8 = 100° ∠3 and ∠8 are alternate exterior angles. Their angles are congruent. So, ∠3 = ∠8 = 100° 3. Find ∠4 if ∠7 = 82° ∠4 and ∠7 are supplementary angles. The sum of their angles equal to 180°, So, ∠4 + ∠7 = 180° ∠4 + 82° = 180° ∠4 = 180° – 82° ∠4 = 98° 3. Find the angle measure Your turn: 1. Find ∠2 if ∠1 = 63° 2. Find ∠3 if ∠8 = 100° 3. Find ∠4 if ∠7 = 82° 3 6 4 7 1 5 2 8