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15. Answer each of the...

15. Answer each of the following:

A Draw a line l and any two points A and B so that ?AB is parallel to the line. Find the image of l under a translation from A to B.

B Draw a line l and any two points A and B so that ?AB is not parallel to l. Construct l', the image of l under the translation from A to B.

We have seen that equilateral triangles, squares, and regular hexago

C. How are l and l' in part (b) related? Why?

ns are the only regular polygons that will tessellate the plane by themselves. However, there are many ways to tessellate the plane by using combinations of these and other regular polygons, as shown in the following figure

1

Try to produce other such tessellations by using the following:

A. Only equilateral triangles, squares, and regular hexagons

B. Regular octagons (8-gons) and squares

A sidewalk is made of tiles of the type shown in the following figure:

Each tile is made of three regular hexagons from which three sides have been removed. Draw a partial tessellation composed of seven such figures.

A group of students on a hiking trip wants to find the distance AB across a pond (see the following figure). One student suggests choosing any point C, connecting it with B, and then finding point D such that ?DCB ?ACB and . How and why does this help in finding the distance AB?

26.

Draw two quadrilaterals such that two angles and an included side in one quadrilateral are congruent, respectively, to two angles and an included side in the other quadrilateral. However, the quadrilaterals are not congruent.

10

Given A, B, and C as vertices, use a compass and a straightedge to construct a parallelogram ABCD:

20.

Some car jacks are constructed like a collapsed rhombus. When used to raise a car, the rhombus is easily seen.

If the sides of the rhombus are 13?, what is the maximum length of the shaft? I haved the figures in the order need

A Draw a line l and any two points A and B so that ?AB is parallel to the line. Find the image of l under a translation from A to B.

B Draw a line l and any two points A and B so that ?AB is not parallel to l. Construct l', the image of l under the translation from A to B.

We have seen that equilateral triangles, squares, and regular hexago

C. How are l and l' in part (b) related? Why?

ns are the only regular polygons that will tessellate the plane by themselves. However, there are many ways to tessellate the plane by using combinations of these and other regular polygons, as shown in the following figure

1

Try to produce other such tessellations by using the following:

A. Only equilateral triangles, squares, and regular hexagons

B. Regular octagons (8-gons) and squares

A sidewalk is made of tiles of the type shown in the following figure:

Each tile is made of three regular hexagons from which three sides have been removed. Draw a partial tessellation composed of seven such figures.

A group of students on a hiking trip wants to find the distance AB across a pond (see the following figure). One student suggests choosing any point C, connecting it with B, and then finding point D such that ?DCB ?ACB and . How and why does this help in finding the distance AB?

26.

Draw two quadrilaterals such that two angles and an included side in one quadrilateral are congruent, respectively, to two angles and an included side in the other quadrilateral. However, the quadrilaterals are not congruent.

10

Given A, B, and C as vertices, use a compass and a straightedge to construct a parallelogram ABCD:

20.

Some car jacks are constructed like a collapsed rhombus. When used to raise a car, the rhombus is easily seen.

If the sides of the rhombus are 13?, what is the maximum length of the shaft? I haved the figures in the order need

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