# Lesson 6 Pythagoras by Proportions Practice Understanding

### 1.

Determine which of the triangles below are similar and which are congruent. Justify your conclusions. Give your reasoning for the triangles you pick to be similar and congruent.

### 2.

Using the right triangle with altitude drawn to the hypotenuse, prove the Pythagorean theorem,

Find the missing values for each right triangle including the length of the altitude.

### 3.

### 4.

### 5.

### 6.

In each problem, find the missing values using the similar triangles, parallel lines, and proportional relationships. Write a proportion and solve.

### 7.

### 8.

For questions 9–12, use the grids provided to determine the indicated segment measures and the proportions.

### 9.

#### a.

When a line is drawn parallel to

#### b.

What is the ratio of the lengths of the two segments created by point

### 10.

#### a.

When a line is drawn parallel to

#### b.

What is the ratio of the lengths of the two segments created by point

### 11.

Place point

### 12.

Place point

Analyze each table closely and determine the missing values based on the given information and values in the table. Create an explicit function rule for the sequence.

### 13.

An Arithmetic Sequence

Term | ||||
---|---|---|---|---|

Value |

Explicit function rule:

### 14.

A Geometric Sequence

Term | ||||
---|---|---|---|---|

Value |

Explicit function rule:

### 15.

An Arithmetic Sequence

Term | ||||
---|---|---|---|---|

Value |

Explicit function rule:

### 16.

A Geometric Sequence

Term | ||||
---|---|---|---|---|

Value |

Explicit function rule: