# Lesson 5Parallelism Preserved and ProtectedSolidify Understanding

### 1.

Use what you know about triangles to write a paragraph proof that proves the sum of the angles in a quadrilateral is . Support your justification with a diagram.

### 2.

Find the measure of in quadrilateral .

For problems 3–7, use the graph of lines , , , and .

### 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 and .

### 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 .

## Set

### 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 , corresponding line segments in a pre-image and its image are parallel or lie on the same line.

#### 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.

## Go

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

### 14.

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

Translate ,

### 16.

Rotate counterclockwise around the point

### 17.

Reflect over the line

Translate ,