Angles
The interior angles of a triangle sum to ______, which is called the _______________________.
180; The Triangle Angle-Sum Theorem
a=b
b=c
Therefore, a=c
Transitive property
Opposite angles of a parallelogram are _________
Congruent
A triangle has side lengths of 3,17, and _________.
What are the possibilities in interval notation?
(14, 20)
Sin=
Opposite/hypotenuse
State the isosceles triangle theorem as an if-then statement.
If a triangle has two congruent sides, then the angles opposite these sides are congruent
Provide an example of the law of detachment
If a, then b is true.
And a becomes true.
Then b will happen.
A rhombus is different from a square in that _____________
A rhombus has four congruent sides, but not necessarily all right angles.
When is a triangle a regular polygon?
regular polygon=congruent sides and angles
An equilateral triangle is a regular polygon.
Cos=
adjacent/hypotenuse
The exterior angle of a 17-gon sum to
360 (always)
a=a
Supplementary
State the triangle midsegment theorem as an if-then statement.
If a line connects the midpoints of any two sides of a triangle, the line will be parallel and half the length of the third line
Tan=
opposite/adjacent
Linear pairs are _________, and you can identify them because ____________________
supplementary; form a line
If a=b, then b=a
A parallelogram contains______________
Two pairs of parallel lines
Name all types of triangle congruence
HL (hypotenuse-leg)
ASA
AAS
SSS
SAS
An isosceles right triangle has leg lengths of a. What is the hypotenuse length?
Vertical angles are ___________, and you can identify them because they are _____________.
Congruent; opposite one another when two lines intersect.
Provide an example of the law of syllogism
If q, then r
Therefore: if p, then r
The diagonals of a parallelogram ___________
Bisect one another
After proving two triangles are congruent, you can use ______________.
CPCTC (corresponding parts of congruent triangles are congruent)
The angles in a right triangle are 90, 30, 60. What are the lengths of each side if the shortest side is 3 meters long?
shortest side = 6
hypotenuse = 12
medium side = 6*square root of 3