Types of Symmetry

We will learn about all types of symmetry of various shapes in geometry. The explanation will help us to understand the different types of symmetrical shapes which possess or does not possess linear symmetry, point symmetry and rotational symmetry.

Name and draw the shape which possesses linear symmetry, point symmetry and rotational symmetry?

1. Line segment:

(i) Linear symmetry possesses 1 line of symmetry i.e. perpendicular bisector of PQ

(ii) Point symmetry possesses point symmetry mid-point O of line segment PQ

(iii) Rotational symmetry possesses rotational symmetry of order 2 about O.

2. Rectangle:

(i) Linear symmetry possesses 2 lines of symmetry. Line joins the mid-point of 2 parallel sides.

(ii) Point symmetry possesses point symmetry with point of intersection of diagonals as the centre of symmetry.

(iii) Rotational symmetry possesses rotational symmetry of order 2.

3. Rhombus:

(i) Linear symmetry possesses 2 lines of symmetry i.e. 2 diagonals of the rhombus

(ii) Point symmetry possesses point symmetry with point of intersection of diagonals as the center of symmetry.

(iii) Rotational symmetry possesses rotational symmetry of order 2.

4. Square:

(i) Linear symmetry possesses 4 lines of symmetry, 2 diagonals and 2 lines joining the mid-point of opposite sides.

(ii) Point symmetry possesses point symmetry with point of intersection of diagonal.

(iii) Rotational symmetry possesses rotational symmetry of order 4.

5. Circle:

(i) Linear symmetry possesses infinite lines of symmetry of order 4

(ii) Point symmetry possesses point symmetry about the center O

(iii) Rotational symmetry possesses rotational symmetry of an infinite order


2. Name and draw the shape which possesses linear symmetry but no point symmetry and rotational symmetry?

1. An angle:

(i) Linear symmetry possesses 1 line of symmetry i.e. angle bisector

(ii) No point symmetry

(iii) No rotational symmetry

2. An isosceles triangle:

(i) Linear symmetry possesses 1 line of symmetry i.e. perpendicular bisector l.

(ii) No point symmetry

(iii) No rotational symmetry

3. Semi-circle:

(i) Linear symmetry possesses 1 line of symmetry i.e. perpendicular bisector of the diameter XY

(ii) No point symmetry

(iii) No rotational symmetry

4. Kite:

(i) Linear symmetry possesses 1 line of symmetry i.e. diagonal QS

(ii) No point symmetry

(iii) No rotational symmetry

5. Isosceles trapezium:

(i) Linear symmetry possesses 1 line of symmetry. Line XY joins the mid-point of 2 parallel sides.

(ii) No point symmetry

(iii) No rotational symmetry

3. Name and draw the shape which possesses linear symmetry and rotational symmetry but no point symmetry?

Equilateral triangle:

(i) Linear symmetry possesses 3 lines of symmetry i.e. the 3 medians of the triangle.

(ii) No point symmetry

(iii) Rotational symmetry possesses rotational symmetry of order 3.

4. Name and draw the shape which does not possess linear symmetry, point symmetry and rotational symmetry?

Scalene triangle:

(i) No linear symmetry

(ii) No point symmetry

(iii) No rotational symmetry

5. Name and draw the shape which does not possess linear symmetry but possesses point symmetry and rotational symmetry?

Parallelogram:

(i) Linear symmetry: No linear symmetry

(ii) Point symmetry possesses point symmetry with point of intersection o

Four-day school week can improve academic performance, study finds

Shortening the school week to four days has a positive impact on elementary school students' academic performance in mathematics, according to researchers at Georgia State University and Montana State University.

The study, published in the journal Education, Finance and Policy in July, analyzed the impact of a four-day school week on student achievement by comparing fourth-grade reading and fifth-grade math test scores from the Colorado Student Assessment Program (CSAP) for students who participated in a four-day school week, versus those who attended a traditional five-day school week.
The researchers found a four-day school week had a statistically significant impact on math scores for fifth-grade students, while reading scores were not affected.
The study suggests there is little evidence that moving to a four-day week compromises student academic achievement, an important finding for U.S. school districts seeking ways to cut costs without hampering student achievement.
"What interested me about our results is they were completely opposite to what we anticipated," said Mary Beth Walker, dean of the Andrew Young School of Policy Studies at Georgia State. "We thought that especially for the younger, elementary school kids, longer days on a shorter school week would hurt their academic performance because their attention spans are shorter. Also, a longer weekend would give them more opportunity to forget what they had learned."
Although the shortened school week did not have a measurable impact on reading outcomes, "the idea that the change in the calendar did not have negative effects we thought was an important result," Walker said.
A number of school districts in the United States have moved from the traditional Monday through Friday schedule to a four-day week schedule as a cost-saving measure to reduce overhead and transportation costs.
Four-day weeks have been in place for years in rural school districts in western states, particularly in Colorado, New Mexico and Wyoming. Over one-third of the school districts in Colorado have adopted a four-day schedule. The alternative schedule has also been considered in school districts in Oregon, Missouri, Florida and Georgia.
The four-day school week requires school districts to lengthen the school day to meet minimum instructional hour requirements. Previously, there was a lack of information on whether the four-day school week affects student performance, Walker said.
The researchers have speculated on why the shortened school week positively affected students but there are not enough data to draw definite conclusions.
"We thought the longer days might give teachers an opportunity to use different kinds of instructional processes," Walker said. "We also speculated that a four-day school week lowered absenteeism, so students who had dentist's appointments or events might be able to put those off until Friday and not miss school. We thought there might be less teacher absenteeism.
"My own personal hypothesis is teachers liked it so much--they were so enthusiastic about the four-day week--they did a better job. There's some evidence in other labor studies that four-day work weeks enhance productivity."
Walker notes the results are only applicable to smaller and more rural school districts. Further studies should be performed to understand the effects on urban school districts, she said.

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Story Source:
The above post is reprinted from materials provided by Georgia State University. Note: Materials may be edited for content and length.

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Journal Reference:

1. D. Mark Anderson, Mary Beth Walker. Does Shortening the School Week Impact Student Performance? Evidence from the Four-Day School Week. Education Finance and Policy, 2015; 10 (3): 314 DOI: 10.1162/EDFP_a_00165#.Vd3cGGA7_Js.