Geometry Help
2/2/2021 MyOpenMath
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Homework: B Parallel Lines and Perpendicular Line Joseph Sigmon
Question 1 0/1 pt 5 99
Question 2 1/1 pt 4 99
Question 3 1/1 pt 4 99
Choose the correct words to fill in the blanks below.
exterior supplementary parallel perpendicular transversal interior corresponding congruent transitive
1. Two or more lines that lie in the same plane are lines if they have no
points in common. 2. A is a line that intersects two or more lines in the same plane at
different points. 3. Angles that lie between two parallel lines are called angles, whereas,
angles that lie outside the parallel lines are called angles.
4. If two parallel lines are cut by a transversal, consecutive interior angles are .
5. angles are angles that correspond to or "match" each other.
6. If any two angles are , their measures are equal.
7. The property says that if and , then
. 8. Two lines are if and only if a right angle is formed at their intersection.
m∠A ≅m∠B m∠B ≅m∠C
m∠A ≅m∠C
Use the figure below to fill in the blank.
and are angles.∠1 ∠8 alternate exterior
Use the figure below to fill in the blank
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Question 4 1/1 pt 4 99
Question 5 1/1 pt 3 99
Use the figure below to fill in the blank.
and are angles.∠4 ∠5 alternate interior
Use the figure below to fill in the blank.
and are angles.∠3 ∠5 consecutive interior
For the problem, find the measure of the angle using the given information and the figure below.
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Question 6 1/1 pt 1 99
Question 7 0/1 pt 5 99
140
m∠2 = 40 ∘
m∠5 =
For the problem, find the measure of the angle using the given information and the figure below.
m∠2 = 52 ∘
m∠3 = 52
For the problem, find the measure of the angle using the given information and the figure below.
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Question 8 0/1 pt 5 99
Question 9 0/1 pt 5 99
`m angle 4=3( m angle 6)`
`m angle 4=`
Use the theorems of parallel lines to solve for `x` in the following.
`x=`
`(14 x-4)^@`
`(8 x+8)^@`
Find the value of `x` that makes `l_1 ∥ l_2`.
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Question 10 0/1 pt 5 99
Question 11 1/1 pt 2-3 99
`x=`
`28^@``x`
Find the value of `x` that makes `l_1 ∥ l_2`.
`x=`
`(12 x+1)^@`
`(7 x+8)^@`
Prove the Alternate Interior Angle Converse.
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Question 12 1/1 pt 1-3 99
Question 13 1/1 pt 1-2 99
Steps Reasons `1.` `angle3~=angle6` Given
`2.` `angle3~=angle2`
`3.` `angle6~=angle2`
`4.` `l_1 ∥ l_2`
`1` `2` `3` `4`
`5` `6` `7` `8`
Vertical Angles Theorem
Transitive Property of Congruence
Corresponding Angles Postulate
Prove the Consecutive Interior Angles Converse.
Steps Reasons `1.` `angle4` and `angle6` are supplements`` Given
`2.` `angle3` and `angle4` are supplements``
`3.` `angle3~=angle6`
`4.` `l_1 ∥ l_2`
`1` `2` `3` `4`
`5` `6` `7` `8`
Linear Pair Postulate
Congruent Supplements Theorem
Alternate Interior Angle Converse
Prove the Alternate Exterior Angles Converse.
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Question 14 1/1 pt 4 99
Question 15 1/1 pt 4 99
Steps Reasons `1.` `angle1 ~= angle8` Given
`2.` `angle1~=angle4`
`3.` `angle4~=angle8`
`4.` `l_1 ∥ l_2`
`1` `2` `3` `4`
`5` `6` `7` `8`
Vertical Angles Theorem
Transitive Property of Congruence
Alternate Interior Angle Converse
Which lines are parallel? Figure is not drawn to scale.
`BC` and `AE`
`AB` and `AE`
`BC and AD`
None
`104^@` `56^@`
`48^@`
Use the information provided in the figure to find the value of `x`.
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Question 16 1/1 pt 2-4 99
Question 17 1/1 pt 1-3 99
Note: Figure not necessarily drawn to scale.
`x=` 43
`47^@`
`x^@`
Prove the following statement: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Steps Reasons `1.` `angle1~=angle2` Given `2.` `angle1` and `angle2` are linear pairs Given
`3.` `mangle1+mangle2=180^@`
`4.` `mangle1+mangle1=180^@`
`5.` `2mangle1=180^@`
`6.` `mangle1=90^@`
`7.` `angle1` is a right angle
`8.` `a ⊥ b`
`angle1`̀ angle2`
Linear Pair Postulate
Substitution Property of Equality
Distributive Property
Division Property of Equality
Definition of Right Angles
Definition of Perpendicular Lines
Prove the following statement: If two lines are parallel to the same line, then they are parallel to each other.
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Steps Reasons `1.` `a ∥ b` ; `b ∥ c` Given
`2.` `angle1 ~= angle2` ; `angle2 ~= angle3`
`3.` `angle1 ~= angle 3`
`4.` `a ∥ c`
`a`
`b`
`c`
`1`
`2`
`3`
Corresponding Angles Postulate
Transitive Property of Congruence
Corresponding Angles Converse