Math Test 3

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

What is the circumference divided by the diameter of any circle?

Pi

What is the formula for the circumference of a circle?

Pi x the diameter OR (2)Pi x radius

What is the distance from the center of circle to any point on it?

Radius

Congruent

Same size and same shape

What is the amount by which the image grows or shrinks called?

Scale Factor

What is like a slice of pie (a circle wedge)?

Sector

What is the difference between similarity and congruency?

Similar figures have same shape, whereas congruent figures have same shape AND size.

What are similar triangles?

Similar triangles have the same shape but are just scaled differently. Similar triangles have congruent angles and proportional sides

What is a line perpendicular to the radius that touches ONLY one point on the circle?

The tangent of the circle

What is the center of the circle?

Origin

Always True, Sometimes True, Never True: A radius of a circle can have both endpoints on the circle.

Never True

An angle with its vertex at the center of the circle is what?

A central angle of the circle

When drawing a squiggly line on paper, you have drawn a what?

A curve

How do you get the scale factor?

New length to Old length

A diameter of a circle is a chord of the circle?

Always True

A radius of a circle has a length that is half the length of a diameter of the circle?

Always True

The bisector of an angle is a line of symmetry for the angle?

Always True

The distance between the center of a circle and a point on the circle is the same as the length of a radius?

Always True

The perpendicular bisector of a line segment is a line of symmetry fro the line segment?

Always True

Two circles with the same length for radius are exactly the same size?

Always True

What are the criteria for two triangles to be similar?

Angle, Angle, Angle (all angles are = to corresponding) Angle, Angle (at least 2 are b/c other one will be) Side, Side, Side (sides are proportional to corresponding) Side, Angle, Side (two sides are proportional and angle is equal)

What is a curved line that is part of circumference of a circle

Arc

What is a line segment within a circle that touches 2 points on the circle?

Chord

What is the distance around the circle?

Circumference

What is a feature of congruent figures?

Corresponding parts of the figures have exactly the same geometric measures

What is true about the sides of similar triangles?

Corresponding sides of similar triangles are proportional

What is the longest distance from one end of a circle to the other?

Diameter

What is the transformed figure called?

Dilated Image

How can two shapes be similar?

If the two shapes can be match so that: every pair of corresponding angles have the same size AND the ratios from every pair of corresponding lengths all equal the same value called the scale factor

An angle with its vertex on the circle and its sides along chords of the circle is called a what?

Inscribed angle

What if something has a scale factor of 1?

It is the original image

What if something has a negative scaled factor?

It would be the opposite direction (-2 x 1 = -2)

What is another word for reductions?

Miniatures

What does not matter for similar figures?

Size

A chord of a circle is a diameter of the circle?

Sometimes True

Enlargements and reductions have what?

The exact same shape as the original shape

What if the scale factor is 0?

Then the image would be 1 single point

What is true about the angles of similar triangles?

They are congruent

True or False: Every diameter is also a chord?

True

Definition of Similarity

Two geometrical figures are known as similar figures, if either both the objects have the same shape or one possesses same shape as the mirror image of another. We can say that if two images are similar, then by shrinking or enlarging one image, other can be obtained

What is a dilation?

Where the polygon grows or shrinks but keeps the same overall shape. It's like zooming in or out on a camera.

For two triangles to be similar...

all corresponding angles are equal and all corresponding sides are proportional

If one angle is cut into two angles of the same size, there is an ____________________

angle bisector

Old and New lengths are

arbitrary

What is the formula for the area of the circle?

area = Pi(r^2)

Two or more circles with the same center are said to be ___________

concentric circles

Multiplicative Comparisons are of _______________ ______________

corresponding lengths

Two figures that have the same shape but not the same size are said to be ___________________ _______________

geometrically similar

A _____________ is a half a sphere

hemisphere

A ______________ bisects a line segment into two equal parts.

perpendicular bisector

A __________ is the 3D set of points at a fixed distance from a fixed point. What is the fixed point called?

sphere, center

What are examples of curves in space?

springs and slinky toys

A line that touches a circle in only one point is called a _________ to the circle.

tangent

Two figures are said to be similar if...

the dimensions of two geometrical figures are different, but their shapes are exactly the same

We denote similarity by the symbol called...

the tilde ~


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