# Lesson 8Parallelogram Conjectures and ProofSolidify Understanding

Use a compass and a straightedge to bisect the following line segments.

### 3.

Construct the midpoint, , of . Then connect point to point .

### 4.

Construct the angle bisector of .

### 5.

Construct a square inscribed in the circle.

### 6.

Construct a regular hexagon inscribed in the circle.

## Set

### 7.

Quadrilateral below was formed by sets of intersecting parallel lines. Figure 2 is the image of Figure 1. It has been rotated . Find the center of rotation for Figure 1. Make a list of everything that has been preserved in the rotation. Then make a list of anything that has changed.

Is quadrilateral a parallelogram? How do you know?

### 8.

Given: ,

Prove: Quadrilateral is a parallelogram.

### 9.

Given: and

Prove: Quadrilateral is a parallelogram.

### 10.

Given: Quadrilateral is a parallelogram.

Prove: and

### 11.

Given: is a parallelogram.

is an image of after a rotation about point

is an image of after being reflected over

Prove:

## Go

State whether each statement is true or false. If it is false, explain why or rewrite the statement to make it true.

### 12.

If a triangle is equilateral, then the median and the altitude are the same segments.

### 13.

The perpendicular bisectors of the sides of a triangle also bisect the angles.

### 14.

Some of the angles in a triangle equal .

### 15.

An altitude of a triangle may fall on the exterior of the triangle.

### 16.

The third angle in a triangle is always the supplement to the sum of the other angles.

### 17.

In a right triangle, the acute angles are always complementary.

### 18.

All squares are also rectangles.

### 19.

A rhombus is always a square.

### 20.

If a figure is a trapezoid, then it is also a parallelogram.

### 21.

The diagonals of a rectangle bisect the angles.

### 22.

A parallelogram can have obtuse angles.

### 23.

The figure made by two pairs of intersecting parallel lines is always a parallelogram.

### 24.

All of the angles in a parallelogram can be congruent.

### 25.

A diagonal always divides a quadrilateral into congruent triangles.

### 26.

If a quadrilateral goes through a translation, the sides of the pre-image and image will remain parallel.