Relationships in Triangles
The incenter is equidistant from each __________ of a triangle.
Side
True or False: All rectangles are squares, but not all squares are rectangles.
False
The corresponding angles of two similar figures are ____________.
Congruent
True or False: The ratios sin, cos, and tan are pronounced "sin", "cos", and "tan."
False
A quadrilateral is a...
... polygon with 4 sides.
What is the name of the point of concurrency for a triangles altitudes?
Circumcenter
What is the exterior angle sum of a 19-gon?
360º
Which of the following is not a similarity Theorem?
SSS~, SAS~, SS~, HL~, AA~
SS~
The tangent of an angle is the ratio _____________ over ____________.
Opposite / Adjacent
Given a 30º-60º-90º triangle with a short leg measuring 4 units, what is the length of the hypotenuse?
8 units.
x = 11
What is the name of the quadrilateral that has congruent diagonals & 2 sets of opposite sides congruent?
Rectangle.
If 4 is the geometric mean of 2 and x, what is x?
In this kind of special right triangle, the short leg is half of the hypotenuse, and the long leg is √3 times the short leg.
30º-60º-90º triangle
Given a 30º-60º-90º triangle with a short leg measuring 4 units, what is the length of the long leg?
4√3 units
15 units
If the interior angle sum of a regular polygon is 9720º, what is the number of sides?
52 sides
YZ = 46.2
In a non-right triangle, you are given two sides and a non-included angle. What law will you use to find a missing angle?
Law of Sines
A 7-sided polygon has angle measures 153º, 37º, 210º, 132º, 178º, 80º, and xº. Find x.
x = 110º
Given a triangle ABC, with sides AB=22, AC=18, and BC=30, what is the order of angles from smallest to largest degree?
B, C, A
In rhombus FISH, IS = 8x+3 and FH = 4x+19. What is the perimeter of the rhombus?
140 units.
The right triangle ABC, with right angle B, and altitude BD, has the following measures: AD = 9 and CD = 4. What is the measure of the altitude BD?
BD = 6
The top of a 45-ft tree house has a very long slide to the ground. The angle of depression from the top of the tree house to the bottom of the slide is 75º. How far away is the end of the slide from the base of the tree house? Round to the nearest foot.
167 feet.
In a non-equilateral triangle, the centroid, circumcenter, and orthocenter of a triangle are collinear. What is the name of the line that they form?
The Euler (oil-er) Line