Triangle Relationships
Define both "perpendicular" and "bisector"
Perpendicular:Two lines intersect (like a T) and form 90 degree angles
Bisector: something that splits a segment into two equal halves
Using the variables "a" and "b," what are two ways to represent a ratio?
a/b or a:b
What does it mean when two triangles are congruent?
The two triangles are the same shape and same size
A triangle with one 90 degree angle is classified as this.
Right Triangle
In a right triangle, a2+b2=c2 is called what?
The Pythagorean Theorem
If a line splits an angle into two equal halves then it is called an
Angle Bisector
Simplify the ratio 45:36
5:4
What are two of the five conditions for congruence?
SSS, SAS, ASA, AAS, HL(right triangles)
A triangle with no congruent sides
Scalene!
What is the name of the side ACROSS from the right angle in a right triangle?
The Hypotenuse
A triangle midsegment is __________ to the third side.
a. parallel
b. congruent
c. perpendicular
3/9 = x/27
Solve for X
x= 9
What does CPCTC stand for?
Corresponding Parts of Congruent Triangles are Congruent
What is the sum of the three angles of a triangle always equal to?
180 degrees
In a 45-45-90 Special Right Triangle, what is the value of the hypotenuse if both legs are equal to 5?
5 sqrt 2
If a segment joins the midpoints of two sides of a triangle, then the segment is __________ to the third side
a. twice as long as
b. half as long as
c. as long as
B is correct
1/5=(2x+2)/10
Solve for X
x=3
In an isosceles triangle with two congruent sides, what can you assume about its angles?
It also has two congruent angles
The Exterior Angle Theorem States that the exterior angle of a triangle is equal to:
a. 180 degrees
b. the adjacent angle
c. the sum of the two non-adjacent angles
C is correct.
A right triangle has:
Find the measure of angle x
approximately 53 degrees
If the base of a triangle is equal to (11x-25), and its midsegment is equal to (4x +1), what is the value of x?
Show your work!
x = 9
Two triangles are similar and have a scale factor of 2:3. If a side of the BIGGER triangle is 12, what is the value of the congruent side on the SMALLER triangle?
8
Name the following theorem:
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Converse of the Isosceles Triangle Theorem
The second angle is equal to (3x+4)
What is the measure of the first angle?
Hint: first solve for x
53 degress
In a right triangle, one acute angle measures 60°, and the hypotenuse is 10 cm long.
What is the length of the side adjacent to the 60° angle?
5