Unit 1 Triangle Similarity
These figures are the same shape but not necessarily the same size.
What are SIMILAR FIGURES?
The circumference of any circle divided by its diameter is always equal to this irrational number.
What is pi?
This is a circle inside a figure that touches exactly one point on each side of the figure.
What is an INSCRIBED CIRCLE?
A trigonometric ratio is the ratio of two side lengths of a _____ triangle.
What is RIGHT?
The cross section of a sphere.
What is a CIRCLE?
This postulate states that if two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.
What is the ANGLE-ANGLE (AA) SIMILARITY POSTULATE?
The exact area of a circle with a diameter of 12 ft.
What is 36(pi) ft2.
(Area of a circle = (pi)(r2).)
A circle is circumscribed about a triangle if each ______ of the triangle lies on the circle.
What is VERTEX?
For an acute angle in a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
What is the SINE RATIO?
The result of rotating a rectangle about an adjacent axis.
What is a CYLINDER?
This theorem states that if a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths.
What is the TRIANGLE PROPORTIONALITY THEOREM?
This is a figure that is made up of several simple geometric shapes such as a triangles, rectangles, squares, circles, and semicircles.
What is a COMPOSITE FIGURE?
In a circle, a radius is ________ to a chord if and only if it bisects the chord.
What is PERPENDICULAR?
The tangent of a 45o angle.
What is 1?
If a line is tangent to a circle, then the line is perpendicular to the _____ drawn to the point of tangency.
What is RADIUS?
This theorem states that an angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides.
What is the ANGLE BISECTOR THEOREM?
Cavalieri’s Principle states that if two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal this.
What is VOLUME?
Inscribed Angle Theorem: An angle inscribed in a circle has a measure that equals _____ the measure of its intercepted arc.
What is ONE-HALF?
Each ratio in the __________ is the sine of an angle over the length of its opposite side.
What is the LAW OF SINES?
The population density of a city whose population
is 5,000 people in a land area of 25 mi2.
What is 200 people/mi2?
(population density = population/area)
A skateboarder wants to build a ramp using a 9-inch board for the height and a 30-inch board for the base. What length board will she need for the ramp? Round to the nearest tenth of an inch.
What is 31.3 inches?
(Use the Pythagorean Theorem to solve this problem.)
If two similar solids have the lengths of their corresponding sides in the ratio of t, then the ratio of their volumes is this.
What is t3?
(t = scale factor)
Tangent-Tangent Theorem: If two ______ segments to a circle intersect at a common exterior point, the segments are equal.
What is TANGENT?
For any oblique △ABC, with sides a, b, and c and
angles A, B, and C: a2 = b2 + c2 - 2bc cos A
What is the LAW OF COSINES?
The density of a substance with
mass 10 lb and volume of 200 in2.
What is 0.05 lb/in2?
(density = mass/volume)