Chapter 6: Relationships within Triangles
In a plane, if a point lies on the perpendicular bisector of a segment, then it is __________ to the two endpoints of the segment.
equidistant
360 degrees
If two triangles are similar, then they have the same _______ but not necessarily the same _______.
shape ... size
Write the formula for the Pythagorean theorem.
a2+b2=c2
We can use the ______________ to prove that a line is tangent to a circle.
Pythagorean Theorem
If a point lies in the interior of an angle and is equidistant to the two sides of the angle, then it is on the _____________.
angle bisector
Write out the formula to find the sum of the interior angles of a polygon.
(n-2) 180
The corresponding sides of similar figures are proportional. Each ratio of sides is equal to the _____________.
scale factor
In a 45-45-90 triangle, the hypotenuse is equal to ___________.
the leg times radical 2.
Two tangents of the same circle that share a common external point are _________.
congruent
The incenter of a triangle is equidistant to all three __________ of the triangle.
sides
Opposite angles and opposite sides of a parallelogram are __________.
congruent
If a triangle has two sides intersected by a line ________ to the third side of the triangle, then the intersected sides are split into proportional parts.
parallel
In a 30-60-90 triangle, the long leg is equal to ____________.
the short leg times radical 3.
Fill in the blank to classify arc measures.
A minor arc is _____ < AB < _______ degrees.
A major arc is ______< ACB < _______ degrees.
A semicircle is equal to _______ degrees.
0<AB<180
180<ACB<360
180
The centroid of a triangle is __________ the distance from each vertex to the midpoint of the opposite side.
two-thirds (2/3)
If a quadrilateral is a __________, then it has exactly one pair of opposite angles that are congruent.
kite
The ratio of the perimeters of two similar figures is equal to the _____________.
scale factor
Fill in the blanks for the trigonometric ratios.
Sine = ________/ hypotenuse
Cosine = _________/ hypotenuse
Tangent = opposite/ adjacent
opposite ... adjacent
The measure of a central angle is _______ its arc.
equal to
Write out the formula for finding a Centroid of a triangle when given the coordinates of the vertices.
(x1+x2+x3)/3 , (y1+y2+y3)/3
A parallelogram is a rhombus if and only if its diagonals are __________ and they ___________ a pair of opposite angles.
perpendicular ... bisect
The ratio of the areas of two similar figures is equal to the __________.
scale factor squared (scale factor2)
To find an angle when given two sides of a triangle, you must use the _______________ functions.
Inverse trigonometric
An inscribed angle is equal to __________.
An intercepted arc is equal to __________.
1/2 of the intercepted arc ... two times the inscribed angle.