Lesson 8 Parallelogram Conjectures and Proof Solidify Understanding

Ready

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

1.

Line segment AB

2.

Line segment TS

3.

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

Line segment MS with point H above MS.

4.

Construct the angle bisector of .

Angle XYZ

5.

Construct a square inscribed in the circle.

Circle with center point

6.

Construct a regular hexagon inscribed in the circle.

Circle with center point

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?

Parallel lines BE and CD intersect parallel lines ED and BC. Figure 2 is a rotation of 180 degrees of Figure 1. Figure 1Figure 2

8.

Given: ,

Prove: Quadrilateral is a parallelogram.

Quadrilateral ABCD with diagonals AC and BD intersect at M. MB and MD have one tic mark and MA and MC have two tics.

9.

Given: and

Prove: Quadrilateral is a parallelogram.

Quadrilateral ABCD with Line segment AB and DC with one tic and AD and BC with two tics.

10.

Given: Quadrilateral is a parallelogram.

Prove: and

Parallelogram ARNM

11.

Given: is a parallelogram.

is an image of after a rotation about point

is an image of after being reflected over

Prove:

Parallelogram MARN reflected over MA forming Parallelogram ACEM. Parallelogram MARN rotated around point F on MA to create parallelogram ABDM

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.