# Lesson 5 Parallelism Preserved and Protected Solidify Understanding

### 1.

Use what you know about triangles to write a paragraph proof that proves the sum of the angles in a quadrilateral is

### 2.

Find the measure of

For problems 3–7, use the graph of lines

### 3.

Find the equation of each line.

### 4.

Which, if any, of the lines are parallel? How do you know?

### 5.

Which, if any, of the lines are perpendicular? How do you know?

### 6.

Find the coordinates of the intersection of lines

### 7.

Classify the shape made by the intersection of the 4 lines.

List as many observations as you can about the shape and its features.

Use the attributes of the shape to find the intersection of lines

and .

### 8.

Verify the parallel postulates below by naming the line segments in the pre-image and its image that are still parallel. Use correct mathematical notation.

#### a.

After a translation, corresponding line segments in an image and its pre-image are always parallel or lie along the same line.

#### b.

After a rotation of

#### c.

After a reflection, line segments in the pre-image that are parallel to the line of reflection will be parallel to the corresponding line segments in the image.

Find the complement and the supplement of the given angles. It is possible that the angle does not have a complement or supplement.

### 9.

### 10.

### 11.

### 12.

### 13.

### 14.

Perform each transformation, given the pre-image and description or rule.

### 15.

Translate

### 16.

Rotate

### 17.

Reflect

### 18.

Translate