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# Copy of Geometry Scavenger Hunt Project Revisited

Shatorupa G. Lucas C and Mohammed A

by

Tweet## mohammed abdulhadi

on 7 April 2013#### Transcript of Copy of Geometry Scavenger Hunt Project Revisited

By: Lucas Chen, Shatorupa Ghosh, and Mohammed Abdulhadi. photo (cc) Malte Sörensen @ flickr Sphere Arcs Meh. The End Geometry Scavenger Hunt Project Table of Contents 1. Rectangular Prism

2. Arc

3. Sphere

4. Hexagon

5. Diameter of a Circle

6. Parallel Lines

7. Perpendicular Lines

8. Equilateral Triangle

9. Cylinder

10. Semicircle

11. Right Angles

12. Square Rectangular Prism Formulas to Remember l= length w=width h=height 1. Volume= lwh

2. Lateral Area= 2h(w+l)

3. Surface Area= 2( lh+ lw + wh) Other Facts Definition: A 3D object which has six faces that are rectangles. It's cross section is a rectangle.

It has 12 sides, 12 edges, 6 faces and 8 vertices.

It could possibly be a cube.

Sometimes, dealing with these types of prisms can get quite edgy! Formulas/ Theorems/ Postulates to Remember 1. Arc Addition Postulate- The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

2. Arc Length- The length of an arc of a circle is the product of the measure of the arc divided by 360 and the circumference of the circle.

3. A theorem- In a circle, a radius perpendicular to a chord bisects the chord and the arc.

4. Another theorem- In the same circle, or congruent circles, congruent central angles have congruent arcs.

5. Another theorem- In a circle, inscribed angles that intercept the same arc are congruent. Other Facts Definition: A part of the circumference of a circle

Minor arc- Arc that is smaller than a semicircle.

Major arc- Arc that is larger than a semicircle.

Adjacent arcs- arcs of the same circle that have exactly one point in common.

Arc length- a fraction of a circle's circumference.

Congruent arcs- Arcs that have the same measure AND are in the same circle or in congruent ones. Formulas to Remember r= radius 1. Surface Area= 4 (pi) (r squared)

2. Volume= 4/3 (pi) (r cubed)

3. Lateral Area= Surface Area Other Facts Definition: the set of all points in space equidistant from a given point. Great Circle- If the center of the cross section ( a circle) is also the center of the sphere.

Spheres have no edges, nor vertices.

The sphere is a locus from a point in space.

A sphere is perfectly symmetrical around the center. Hexagon Formulas to Remember Area=1/2 (apothem) (perimeter)

Perimeter= 6(Side)

Area could be approximately calculated by 2.59(Side) Known Facts Definition: A 6-sided polygon

If you were to divide it into 6 equivalent portions, each central angle would be 60 degrees.

The pronoun Hexa- means 6.

The sum of all interior angles is 720. Duh, this means each interior angle is 120. Diameter of a Circle Formulas to Remember Other Facts Parallel Lines Formulas/ Postulates/ Theorems to Remember r=radius c=circumference a=area To find the diameter from the circumference, divide the circumference by pi, making the formula look like this: c/pi=diameter To find the diameter from the area, divide the area by pi, take the square root of that and multiply by 2. Or, in other words, square root of (a/pi) times 2 = diameter. Definition: A straight line going through the center of a circle connecting two points on the circumference. Converse of the Corresponding Angles Postulate- If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

Converse of the Alternate Interior Angles Theorem- If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Converse of the Same-Side Interior Angles Theorem- If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

If two lines are parallel to the same line, then they are parallel to each other.

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Parallel Postulate- Through a point not on a line, there is one and only one line parallel to a given line. Other Facts Definition: Two lines on a plane that never meet.

Parallel lines go in the same direction.

They are always the same distance apart.

One tip to help you remember that parallel lines never intersect is to look at the double l's in the work parallel. L's never meet, therefore when you see the word parallel, notice the double l's and you will remember that parallel lines never intersect, like l's don't either. Perpendicular Lines Different Facts Definition: Lines that form a right angle with each other.

The wall and the floor are perpendicular to each other.

Perpendicular lines always intersect at least one point! xD

Perpendicular lines have always negative reciprocal slopes.

The sign of the perpendicular line is like an upside down T.

The adjacent sides of a rectangle or a square are perpendicular to each other. The diameter is the longest chord that can be on a circle.

The diameter is twice the radius, or 2r.

The tangents at the end of a diameter are parallel.

If you rotate a diameter 180 degrees, it is going to cover the whole area of the circle.

The integral of a circle to 180 degrees is the area of the circle.

Diameter is the only chord that has rotational symmetry against the center. Equilateral Triangle Formulas to Remember b=base h=height s=side Area= 1/2bh

Perimeter= 3s Other Facts Definition: A triangle with equal sides of length.

All angles would be equiangular.

The measure of each angle would be 60°.

The prefix Equi- means equal. Cylinder Formulas to Remember r= radius h=height d= diameter Surface Area= 2πrh +2π(rsquared)

Lateral Area= 2πrh or 2πd

Perimeter= circumference of bases+ dimensions of rectangle

Volume= 2π(r squared)h Other Facts Definition: A solid geometric figure with straight parallel sides and a circular or oval section.

Altitude of a cylinder- a perpendicular segment that joins the planes of the bases. It is more commonly known as the height of the cylinder.

A cylinder is made up of two circles and a rectangle.

Oblique cylinder- the segment joining the centers of the bases is not perpendicular to the planes containing the bases. Semi-Circle Formulas to Remember r=radius d=diameter c=circumference a=area Area= 2π(r squared) ÷ 2

Circumference= 2πd ÷ 2 Other Facts Definition: Half a circle Right Angles Interesting Facts Definition: An angle which is equal to 90°.

There are 4 right angles in a square and rectangle.

Right angles are formed by perpendicular lines.

The supplimentary angle of a right angle is a right angle.

A right angle is a quarter of a turn. Square Formulas to Remember l=length w=width s=side Area= lw or s squared.

Perimeter= l+l+w+w or 2(w+l) or 4s. Known Facts Definition: 2D object with four sides that are equivalent.

4 90° angles.

A square is also a rectangle.

All diagonals are congruent. It always measures 180 degrees.

The longest "chord" of a semicircle is its radius.

Oh yeah one more: Its Humpty Dumpty's head! Thanks for Watching!

Full transcript2. Arc

3. Sphere

4. Hexagon

5. Diameter of a Circle

6. Parallel Lines

7. Perpendicular Lines

8. Equilateral Triangle

9. Cylinder

10. Semicircle

11. Right Angles

12. Square Rectangular Prism Formulas to Remember l= length w=width h=height 1. Volume= lwh

2. Lateral Area= 2h(w+l)

3. Surface Area= 2( lh+ lw + wh) Other Facts Definition: A 3D object which has six faces that are rectangles. It's cross section is a rectangle.

It has 12 sides, 12 edges, 6 faces and 8 vertices.

It could possibly be a cube.

Sometimes, dealing with these types of prisms can get quite edgy! Formulas/ Theorems/ Postulates to Remember 1. Arc Addition Postulate- The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

2. Arc Length- The length of an arc of a circle is the product of the measure of the arc divided by 360 and the circumference of the circle.

3. A theorem- In a circle, a radius perpendicular to a chord bisects the chord and the arc.

4. Another theorem- In the same circle, or congruent circles, congruent central angles have congruent arcs.

5. Another theorem- In a circle, inscribed angles that intercept the same arc are congruent. Other Facts Definition: A part of the circumference of a circle

Minor arc- Arc that is smaller than a semicircle.

Major arc- Arc that is larger than a semicircle.

Adjacent arcs- arcs of the same circle that have exactly one point in common.

Arc length- a fraction of a circle's circumference.

Congruent arcs- Arcs that have the same measure AND are in the same circle or in congruent ones. Formulas to Remember r= radius 1. Surface Area= 4 (pi) (r squared)

2. Volume= 4/3 (pi) (r cubed)

3. Lateral Area= Surface Area Other Facts Definition: the set of all points in space equidistant from a given point. Great Circle- If the center of the cross section ( a circle) is also the center of the sphere.

Spheres have no edges, nor vertices.

The sphere is a locus from a point in space.

A sphere is perfectly symmetrical around the center. Hexagon Formulas to Remember Area=1/2 (apothem) (perimeter)

Perimeter= 6(Side)

Area could be approximately calculated by 2.59(Side) Known Facts Definition: A 6-sided polygon

If you were to divide it into 6 equivalent portions, each central angle would be 60 degrees.

The pronoun Hexa- means 6.

The sum of all interior angles is 720. Duh, this means each interior angle is 120. Diameter of a Circle Formulas to Remember Other Facts Parallel Lines Formulas/ Postulates/ Theorems to Remember r=radius c=circumference a=area To find the diameter from the circumference, divide the circumference by pi, making the formula look like this: c/pi=diameter To find the diameter from the area, divide the area by pi, take the square root of that and multiply by 2. Or, in other words, square root of (a/pi) times 2 = diameter. Definition: A straight line going through the center of a circle connecting two points on the circumference. Converse of the Corresponding Angles Postulate- If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

Converse of the Alternate Interior Angles Theorem- If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Converse of the Same-Side Interior Angles Theorem- If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

If two lines are parallel to the same line, then they are parallel to each other.

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Parallel Postulate- Through a point not on a line, there is one and only one line parallel to a given line. Other Facts Definition: Two lines on a plane that never meet.

Parallel lines go in the same direction.

They are always the same distance apart.

One tip to help you remember that parallel lines never intersect is to look at the double l's in the work parallel. L's never meet, therefore when you see the word parallel, notice the double l's and you will remember that parallel lines never intersect, like l's don't either. Perpendicular Lines Different Facts Definition: Lines that form a right angle with each other.

The wall and the floor are perpendicular to each other.

Perpendicular lines always intersect at least one point! xD

Perpendicular lines have always negative reciprocal slopes.

The sign of the perpendicular line is like an upside down T.

The adjacent sides of a rectangle or a square are perpendicular to each other. The diameter is the longest chord that can be on a circle.

The diameter is twice the radius, or 2r.

The tangents at the end of a diameter are parallel.

If you rotate a diameter 180 degrees, it is going to cover the whole area of the circle.

The integral of a circle to 180 degrees is the area of the circle.

Diameter is the only chord that has rotational symmetry against the center. Equilateral Triangle Formulas to Remember b=base h=height s=side Area= 1/2bh

Perimeter= 3s Other Facts Definition: A triangle with equal sides of length.

All angles would be equiangular.

The measure of each angle would be 60°.

The prefix Equi- means equal. Cylinder Formulas to Remember r= radius h=height d= diameter Surface Area= 2πrh +2π(rsquared)

Lateral Area= 2πrh or 2πd

Perimeter= circumference of bases+ dimensions of rectangle

Volume= 2π(r squared)h Other Facts Definition: A solid geometric figure with straight parallel sides and a circular or oval section.

Altitude of a cylinder- a perpendicular segment that joins the planes of the bases. It is more commonly known as the height of the cylinder.

A cylinder is made up of two circles and a rectangle.

Oblique cylinder- the segment joining the centers of the bases is not perpendicular to the planes containing the bases. Semi-Circle Formulas to Remember r=radius d=diameter c=circumference a=area Area= 2π(r squared) ÷ 2

Circumference= 2πd ÷ 2 Other Facts Definition: Half a circle Right Angles Interesting Facts Definition: An angle which is equal to 90°.

There are 4 right angles in a square and rectangle.

Right angles are formed by perpendicular lines.

The supplimentary angle of a right angle is a right angle.

A right angle is a quarter of a turn. Square Formulas to Remember l=length w=width s=side Area= lw or s squared.

Perimeter= l+l+w+w or 2(w+l) or 4s. Known Facts Definition: 2D object with four sides that are equivalent.

4 90° angles.

A square is also a rectangle.

All diagonals are congruent. It always measures 180 degrees.

The longest "chord" of a semicircle is its radius.

Oh yeah one more: Its Humpty Dumpty's head! Thanks for Watching!