Vertical+Angles+Theorum,+4

Vertical Angles Theorem Sarah K, Anna M, Abby G, and Sibel A - Fri Period 4

Definition: Vertical angles that are congruent.



The roads Ville and Center intersect with each other and form a vertical angle. A vertical angle is made when lines cross each other to create 2 opposite rays, and an opposite ray is formed when a point lies between 2 other points at the same time. As a result of Ville and Center crossing each other 4 angles are made; <R, <A, <B, and <S. According to the Vertical Angles Theorem, <R and <B are congruent to each other and <S and <A are congruent to each other as well.



True and False 1. A and C are congruent angles 2. A and B are complementary angles 3. D and C are congruent angles 4. B and C are a linear pair

Answers 1. True - A is across from C so the measurements of angles are the same and thus congruent, meaning that they have the measurements - this is supported by the definition of congruent angles 2. False - <A + <B adds up to 180 degrees as they are on the same line which means that they are supplementary - this is supported by the definition of supplementary angles 3. False - D and C are not across from each other in the vertical angle which would make them congruent - this is supported by the definition of congruent angles 4. True - B and C are on the same line which means that they're a linear pair - this is supported by the definition of a linear pair



1. answer: explanation: This is a vertical angle so that means that the measurement of 1 angle is is also the measurement of the angle directly across from it, in this problem step by step procedure:
 * 1) 2. When given this vertical angle and told that answer:  explanation: <C is across from <A which according to the Vertical Angle Theorem means that <C = <A. The hippo thought that <A was supplementary to <C and so used the equation <A + <C = 180 degrees, this was wrong however as <A and <C are not supplementary to each other as they are not on the same line. step by step procedure:
 * 1) <A = 82 degrees
 * 2) <A = <C
 * 3) <C = 82 degrees

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1. If angle b is equal to 97'. What does <d equal? --Answer is 83'. This is 83 because <b and <d are congruent and equal the same, as well as <a and <c. <b and <c also equal to 180, as do <a and <d. So if <b = 97' and <d is congruent, which means it equals the same so 180-97=83. So <s a and c are equal to 83'.

True and false

2. < c and <d is a linear pair.

-- Answer- true. This is true because <c and <d are on the same line which means that they're a linear pair, we know this because of the definition of a linear pair.

3. <a and <c congruent.

--Answer- true. This is true because <a is across from <c so the measurements of angles are the same which means there congruent. We know this because of the definition of congruent angles.

VERTICAL ANGLES Given: Angle 1 = 103 degrees.

1. Angle 1 is congruent to Angle 3. 2. Angle 2 = 103 degrees. 3. Angle 4 = 77 degrees. 4. Angle 3 = 77 degrees. 5. Angle 1 is congruent to Angle 2.
 * True and False**

Answers: 1. True, because according to the vertical angles congruence theorem, the vertical angles (or the angles that are directly across from each other), are always congruent. 2. False, because Angle 1 equals 103 degrees, so saying that Angle 2 equals 103 degrees is like saying that an angle measures 206 degrees, which is impossible. Together, Angle 1 and Angle 2 must equal 180 degrees, so Angle 2 must be 77 degrees according to the given 103 degree label of Angle 1. 3. True, because together Angle 3 & 4 equal 180 degrees. 4. False, because together Angle 3 & 4 do not equal 180 degrees. 5. False, because Angle 1 & 2 are not vertical angles. They are indeed a linear pair, but only vertical angles (or angles that are directly across from each other) are congruent. (Angle 2 is equal to 77 degrees)