# Lesson 6Pythagoras by ProportionsPractice 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.

## Set

### 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.

## Go

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

### 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 through point , where will it intersect ?

#### b.

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

### 10.

#### a.

When a line is drawn parallel to through point , where will it intersect ?

#### b.

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

### 11.

Place point on the segment to split it into two segments with lengths that are a ratio of .

### 12.

Place point on the segment to split it into two segments with lengths that are a ratio of .

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 $1$ $2$ $3$ $4$ $7$ $22$

Explicit function rule:

### 14.

A Geometric Sequence

 Term Value $1$ $2$ $3$ $4$ $7$ $56$

Explicit function rule:

### 15.

An Arithmetic Sequence

 Term Value $5$ $6$ $7$ $8$ $10$ $43$

Explicit function rule:

### 16.

A Geometric Sequence

 Term Value $7$ $8$ $9$ $10$ $3$ $24$

Explicit function rule: