Chapter 5.CT, Problem 16CT

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*In Exercises 16 and 17, complete the statements and reasons in each proof.*

*Given: *

*Prove: *

Statements |
Reasons |

1._______________ 2. 3._______________ 4. |
1.____________________ 2. If 2|| lines are cut by a transversal,________ 3. Identity 4._____________________ |

To determine

**To complete:**

The missing statements and reasons.

Explanation

Given:

To prove:

Given figure,

Statements |
Reasons |

1. ________________ 2. 3. _________________ 4. |
1. ___________________ 2. If 2|| lines are cut by a transversal, ________ 3. Identity 4. _____________________ |

Proof:

Consider the triangles *MNP *and *QRP,*

Given,

If two parallel lines (

Therefore,

Here,

**By AA theorem:**

If the two angles of one triangle are congruent to the two angles of another triangle, then the triangles are similar.

Here,

Therefore, By AA theorem the triangles

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