Alternate Exterior Angles Theorem states that "Alternate Exterior Angles formed by two parallel lines and a transversal are always congruent".

In the figure given above, angles 2 and 8 are alternate exterior angles. Angles 1 and 7 are also alternate exterior angles. Therefore, $\angle$2 = $\angle$8 and $\angle$1 = $\angle$7.

One way to easily find the alternate exterior angles is that they are the vertical angles of the alternate interior angles. Alternate exterior angles are equal to one another.

Related Calculators | |

Bayes Theorem Calculator | Binomial Theorem Calculator |

Calculate Pythagorean Theorem | De Moivre's Theorem Calculator |

If two parallel line segments or rays are cut by a transversal, the alternate exterior angles are congruent.

**Given:**

Line p is parallel to line q with the transversal l, as shown in the figure given below.

**Proof:**

S.No. | Statement | Reasons |

1 | p | | q with the transversal l | Given |

2 | $\angle$2 is congruent to $\angle$6 | Parallel Lines Postulate |

3 | $\angle$6 is congruent to $\angle$8 | Vertical Angle Theorem |

4 | $\angle$2 is congruent to $\angle$8 | Using Transitive Property |

Therefore, the alternate exterior angles are congruent.

Hence Proved.

**Proof:**

S.No. |
Statement |
Reasons |

Step 1: |
$\angle$2 is congruent to $\angle$8 |
Given |

Step 2: |
$\angle$6 is congruent to $\angle$8 |
Vertical Angle Theorem |

Step 3: | $\angle$2 is congruent to $\angle$6 |
Corresponding Angles |

Step 4: |
p | | q with the transversal l |
From Step 2 and Step 3 Parallel Line Postulate |

Therefore, the lines are parallel.

Hence Proved.Given below are some of the examples on alternate exterior angles theorem.

Therefore, b + 65$^o$^{} = 180$^o$^{} => b = 180$^o$^{} - 65$^o$^{} = 115$^o$^{}

Therefore, c = b = 115$^o$^{}

Therefore, d = 65$^o$^{}

Therefore, e = d = 65$^o$^{}

Therefore, f + 65$^o$ = 180$^o$ => f = 180$^o$ - 65$^o$^{} = 115$^o$^{}

Therefore, g = f = 115$^o$^{}

Therefore, h = e = 65$^o$

Related Topics | |

Math Help Online | Online Math Tutor |