Abeka Plane Geometry Test 9

T/F If the lengths of corresponding pairs of sides of two polygons are proportional, the polygons are similar

false

T/F If in two triangles, at least one pair of corresponding sides is not proportional, then the triangles are never similar

true

T/F A line through the midpoints of two sides of a triangle cuts off a new triangle that is similar to the original triangle

true

T/F Two triangles are similar if just two pairs of corresponding angles are known to be equal

true

T/F The lengths of two corresponding altitudes of similar triangles will have the same ratio as any pair of corresponding sides

true

T/F The altitude of the hypotenuse of a right triangle is the third proportional between the two segments of the hypotenuse that it forms

false

T/F Doubling the lengths of the sides of similar triangles will also double the ratio of similitude of those triangles

false

If the legs of a right triangle are 6 and 8, then the hypotenuse is what?

10

T/F When a secant and a tangent are drawn to a circle from the same point outside the circle, then the secant is the mean proportional between the tangent and its external segment

false

The locus of points at a given distance from a given point is...

a circle

The locus of points a given distance from a line is...

two straight lines

The locus of centers of all circles having a given line segment as a common chord is...

a straight line

The center of a circumscribed circle about a given triangle may be found by the intersection of...

perpendicular bisectors of the sides

Know...

area of trapezoid formula

area of parallelogram formula

area of triangle formula

know how to construct

a fourth proportional between line segments p. 223

know how to construct

a mean proportional between segments p.225

the ratio of lengths of a pair of corresponding side in two similar triangles...

is equal the ratio of the lengths of the corresponding altitudes

be able to find the fourth proportional of a series of numbers i.e.: 2,4,6,\_________

12

be able to find the length of the tangent to a circle when the tangent to a circle when the tangent and a secant are drawn to a circle from an external point and the secant passes through the center of the circle

the length of the tangent is the square root of (the external secant times the internal secant)

in given quad ABCD, the locus of points of equidistant from AB and AD must include vertex C if ABCD is ...

NOT a trapezoid, rectangle, or parallelogram

if pint C is not on segment AB, how many points are equidistant from on C on AB?

only 2

no points on a segment can be farther apart than the length of the segment

ie: if a segment is 7 inched long, no point can be farther than 7 inches apart on the line segment

know how to construct a point that is equidistant to two points from a line

...

T-Proof