Vocabulary
Lines, rays, or segments that intersect at a 90-degree angle
Perpendicular
When the measures in the conclusion are larger than the measures in the given information, which properties may have been used?
Addition or multiplication
Find the supplement of an angle with the measure 42 degrees, 15 minutes, 38 seconds
137, 44'22"
Complete the following:
The _________ Property states that when an angle is added to two congruent angles, the sums are congruent.
Addition Property
When a point or ray is said to bisect an angle or segment this means ___________________
It divides it into two congruent segments or angles
the vertical number line on a coordinate plane
y-axis
Given: Segments ABC and DEF
AB⩭DE, and BC⩭BF
Prove AC ⩭ DF
addition
Find the complement of the angle with the measure 97
none
The ___________ Property states that if a segment or angle is subtracted from congruent segments or angles, the differences are congruent.
Subtraction
If a problem asks you to find the supplement of an angle, what is a way to represent that algebraically?
180-x
Lines that intersect but do not form a 90-degree angle
oblique lines
Given: m∠DAC = m∠ECA
m∠1 = m∠2
prove: m∠3 = m∠4
Subtraction
One of two complementary angles has a measure that is six more than twice as large as the other. Find the measure of the larger angle
62
Theorem 18 states that vertical angles are __________.
Congruent
What is a clue to telling the difference between the transitive property and substitution?
The transitive property looks like a train, or it reflects chain reasoning, connecting all the given information together to form a conclusion.
Rays that are collinear and point in opposite directions
Opposite rays
Given: RV and SW trisect PT and PX
ST ⩭ WX
Prove: PT ⩭ PX
Multiplication
The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half the complement.
35
Which theorem would be used to prove the following: 1⩭2, 2⩭3, 2⩭4, prove that 1⩭4
Transitive
When drawing conclusions, what is one thing you should look for in the problem?
key words or phrases, given information
Two opposite rays that intersect to form two angles
vertical angles
Given: FG ⩭ JH
N is the Midpoint of FG
O is the midpoint of JH
Prove: NG ⩭ OH
Division
The measure of the supplement of an angle is five times that of the angle's complement. Find the measure of the complement
22.5
What property states that if angles or segments are congruent to the same angle or segment, they are congruent to each other
The Transitive Property
Find the perimiter of triangle VRS
50