Relationships in Triangles
What are the four main "centers" of a triangle?
Centroid, Incenter, Circumference, Orthocenter
If a figure is translated 3 units left and 3 units up. Which translation moves the image back to the original position?
3 units right and 3 units down
Do radicals have to be identical to multiply them?
No. When multiplying radicals, you multiply the coefficients together and the radicands together:
What is the radius of a circle?
the straight-line distance from its exact center to any point on its outer edge
What theorem is not valid theorem to show that two triangles are congruent?
SSA
Is there a rule that connects the size of a triangle's sides to its angles?
Yes. The longest side is always directly opposite the largest angle, and the shortest side is opposite the smallest angle.
Point P' (5,-4) is the image of point P(2,3) under a translation. Select the image of (6,-2) under the same translation.
(9,-9)
How do I divide radicals?
You can divide the radicands if the indices are the same
How do you find the radius of a circle with a given circumference?
To find the radius of a circle from its circumference, simply divide the circumference by 6.28
Can you use AAA (Angle-Angle-Angle) to prove congruence?
No. AAA only proves that two triangles are similar (the same shape but different sizes), not congruent (the same size and shape
What is the Exterior Angle Theorem?
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles
Point T is at (-6,4). What are the coordinates of point T' after a reflections across x=0 and then y =0
(6,-4)
What if the radicals are not the same?
What is diameter in simple terms?
the straight-line distance from one side of a circle (or sphere) to the opposite side, passing exactly through the center.
if two triangles are congruent, does that mean all their parts are congruent
yes
DF is the perpendicular bisector of CE, If CD = 12 and EF = 5, what is the perimeter of CDE?
34 units
How do you find a translated point?
A translation simply slides a shape horizontally and vertically. To find the new coordinates, add or subtract the shifting units from the original coordinates.
What is "rationalizing the denominator" and how do I do it?
you should not leave a radical in the denominator of a fraction. To eliminate it, multiply the numerator and denominator by the radical in the denominator.
What is the measure of any angle inscribed in a semicircle?
It is always 90 degrees
What is an "included" angle or side?
A triangular pendant has sides of length 23mm and 31mm. What are the possible lengths (in whole mm) for the third side?
Between 9mm and 53mm
What are the rules for a reflection over an axis?
A reflection acts as a mirror image of the original figure
No. You can multiply any radicals as long as they have the same index. Multiply the numbers outside together and the numbers inside together, then simplify.
Find the radius of a circle with aa circumference of 106.81 centimeters
R=17
Why doesn't SSA (Side-Side-Angle) work as a congruence theorem?
Because it can create an ambiguous case where two entirely different triangles could be formed using the exact same measurements