3.1-3.2 Use Angle Pairs, Parallel Lines and Transversals Types of Lines In this figure... Vocabulary! Postulates and Theorems Applying Postulates and Theorems Finding Angles Two lines are parallel lines if they do not intersect and are coplanar. BD, AC, BH,and AG are perpendicular to AB. transversal- a line that intersects 2 or more coplanar lines at different points consecutive interior angle- 2 angles formed by 2 lines and a transversal and lie between the 2 lines on the same side of the transversal If angle 1 is 105 find 4, 5, and 8. Madison Blair Two lines are skew lines if they do not intersect and are not coplanar. M N K T U So,

Lines M and N are parallel.

Lines M and K are skew. Planes T and U are parallel B A H G F E C D CD, GH, and EF are parallel to AB CF and EG are skew to AB corresponding angles- 2 angles that are formed by 2 lines and a transversal and occupy corresponding positions alternate interior angles- 2 angles that are formed by 2 lines and a transversal and lie between the two lines and on opposite sides of the transversal alternate exterior angles- 2 angles formed by 2 lines and a transversal and lie outside the 2 lines and on opposite sides of the transversal 1 2 3 4 5 6 7 8 Angles 2 & 6, 1 & 5, 3 & 7, and 4 & 8 are corresponding angles Angles 1 & 8 and 2 & 7 are alternate exterior angles Angles 4 & 5 and 3 & 6 are alternate interior angles Angles 3 & 5 and 4 & 6 are consecutive interior angles Examples! if 2 parallel lines are cut by a transversal then... -the pairs of corresponding angles are congruent -the pairs of alternate interior angles are congruent -then the pairs of alternate exterior angles are congruent -the pairs of consecutive interior angles are supplementary 1 2 5 6 3 4 7 8 These angles are congruent: 1 & 5 1 & 4

2 & 6 2 & 3

3 & 7 5 & 8

4 & 8 6 & 7 These angles are supplementary: 1 & 3 1 & 2

2 & 4 3 & 4

5 & 7 5 & 6

6 & 8 7 & 8 1 2 3 4 5 6 7 8 4= 105

5=105

8=105 Because vertical and corresponding angles are congruent If angle 3 is 68 and angle 8 = ( 2x + 4) what is the value of x? ( angles 3 and 8 are NOT corresponding, vertical, or alternate angles but they are supplementary) So, 68 (2x 4) 180 + + = - 68 -68 = 112 2x+4 -4 -4 2x=108 2 2 x=54 Then you can plug 54 into the equation to find the measure of angle 8 Angle 8= 112 Citations www.mathisfun.com

www.mathwarehouse.com

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# Geometry project

By: Madison Blair

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