Corresponding+Angles+Postulate+and+Consecutive+Interior+Angles+Theorem

Consecutive Interior Angles Theorem:  If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Corresponding Angles Postulate:  If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Examples: use the diagram ** 4) name the angle pair relationship of <3 and <7 ** ** 5) if m<4= 35degrees, what is the m<8=? ** ** 6) if m<2=69degrees, what is the m<6=? ** ** 7) if m<3= 50, what is the m<6=? ** ** Answers: ** ** 1)consecutive interior angles ** ** 2) corresponding angles ** ** 3) consecutive interior angles ** ** 4) corresponding angles ** ** 5) 35degrees ** ** 6) 69degrees ** ** 7) 130degrees ** Websites:   [|Corresponding Angles Postulate]   [|Consecutive Interior Angles Theorem]   [|Games]   [|Crossword Puzzle]      ** Consecutive Interior Angles Theorem and Corresponding Angles Postulate **  Miranda J, Rachel S, Kathleen D, Danielle C
 * Consecutive Interior Angles Theorem and Corresponding Angles Postulate ** ** Kate W., Lena W., Hannah T., Rachel T. **
 * 1) name the angle pair relationship of <3 and <6 **
 * 2) name the angle pair relationship of <1 and <5 **
 * 3) name the angle pair relationship of <4 and <5 **

**Consecutive Interior Angles Theorem**
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.

Consecutive Interior Angles
Consecutive Interior Angles are formed when two [|parallel lines] are cut by a transversal. In the figure, angles 3 and 5 are consecutive interior angles. Also angles 4 and 6 are consecutive interior angles.

Proof:
 * Given:** //k// || //l// is a transversal
 * Prove:** [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image001.gif width="64" height="11" align="bottom"]] are [|supplementary] and [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image002.gif width="66" height="11" align="bottom"]] are supplementary.
 * || **Statement** || **Reason** ||
 * 1 || //k// || //l//, //t// is a traversal. || Given ||
 * 2 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image003.gif width="63" height="11" align="bottom"]] form a linear pair and [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image004.gif width="67" height="11" align="bottom"]] form a linear pair. || ||
 * 3 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image003.gif width="63" height="11" align="bottom"]]are supplementary [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image004.gif width="67" height="11" align="bottom"]] are supplementary. || ||
 * 4 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image005.gif width="141" height="11" align="bottom"]] || ||
 * 5 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image001.gif width="64" height="11" align="bottom"]] are supplementary [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image002.gif width="66" height="11" align="bottom"]] are supplementary. || ||

Answer:

Proof:
 * Given:** //k// || //l// is a transversal
 * Prove:** [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image001.gif width="64" height="11" align="bottom"]] are [|supplementary] and [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image002.gif width="66" height="11" align="bottom"]] are supplementary.
 * || **Statement** || **Reason** ||
 * 1 || //k// || //l//, //t// is a traversal. || Given ||
 * 2 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image003.gif width="63" height="11" align="bottom"]] form a linear pair and [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image004.gif width="67" height="11" align="bottom"]] form a linear pair. || Definition of linear pair ||
 * 3 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image003.gif width="63" height="11" align="bottom"]]are supplementary [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image004.gif width="67" height="11" align="bottom"]] are supplementary. || Supplement postulate ||
 * 4 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image005.gif width="141" height="11" align="bottom"]] || Alternate Interior Angle Theorem ||
 * 5 || [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image001.gif width="64" height="11" align="bottom"]] are supplementary [[image:http://hotmath.com/hotmath_help/topics/consecutive-interior-angle-theorem/consecutive-interior-angle-theorem-image002.gif width="66" height="11" align="bottom"]] are supplementary. || Substitution Property ||

Corresponding Angles Postulate- states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent.

Examples:

Name four corresponding angles.

Answers: <3 and <7 <2 and <6 <4 and <8 <1 and <5