# Exam 2 Exercises

- Author:
- Adam

## Problem 1)

If line segment is 60 units long and contains points

*B, C,*and*D*, in that order, and*B*is the midpoint of*AC*- the ratio of
*CD*to*DE*is 2:3 *D*is the midpoint of*CE*

*Find**AD*.## Problem 2)

What is the

*definition*of perpendicular lines? Hint: Although they form 90-degree angles, this is not the definition.## Problem 3)

Adam believes that every relationship is a transitive relationship. Which of the following is an example which demonstrates that he's wrong?
a) Point

*P*is a distance of 5 from point*Q*, and point*Q*is a distance of 5 from point*R*. b) Triangle*T*is congruent to triangle*U,*and*U*is congruent to*V*. c) Triangle*T*is similar to triangle*U,*and*U*is similar to*V*. d) Number*x*is less than*y*, and*y*is less than*z*.## Problem 4)

If then . This fact is called ______________.

## Problem 5)

a) State the definition of supplementary angles.
b) Could vertical angles be supplementary? If so, what can you infer about them?
c) Could two interior angles in a triangle be supplementary? If so what can you infer about them?
d) State the definition of complementary angles.
e) Could vertical angles be complementary? If so, what can you infer about them?
f) Could two interior angles in a triangle be complementary? If so, what can you infer about the triangle?

## Problem 6)

In the diagram below, are lines. Line is perpendicular to . Angle has measure and has measure and has measure 30-degrees. Find every (small) angle in the picture.

## Problem 7)

In line segment if and and then find the lengths of all segments.

## Problem 8)

Suppose are measures of three angles, where angle is the complement of and where is the supplement of . Is it possible for the ratio of ?

## Problem 9)

Below is a proof of the theorem that all rhombi are parallelograms. Supply the missing statements and reasons.

Statement | Reason |

------------ | ------------- |

1) | Given |

2) | |

3) | |

4) | CPCTC |

5) | Alternate interior angles are congruent |

6) | |

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