Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Angles and Parallel Lines: Finding Relationships and Solving Problems, Lecture notes of Reasoning

Answers and explanations for various angle relationships and proofs related to parallel lines and a transversal. Topics include corresponding angles, supplementary angles, congruent angles, complementary angles, and finding unknown angle measures using theorems and given information.

What you will learn

  • What theorem is used to find the value of an angle based on its corresponding angle?
  • Given two angles, how can you determine if they are congruent or supplementary?
  • How are complementary angles related to perpendicular lines?

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

agrata
agrata 🇺🇸

4

(7)

258 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Findthevalueofthevariable(s)ineachfigure.Explainyour
reasoning.
24.
ANSWER:
y=114bytheCorrespondingAnglesPostulate;x=54bytheSupplement
Theorem
26.
ANSWER:
x=63bytheVerticalAngleTheoremandtheConsecutiveInterior
AnglesTheorem
28.
ANSWER:
x=54bytheAlternateInteriorAnglesTheorem;y=12bythe
ConsecutiveInteriorAnglesTheorem
30.PROOFCopyandcompletetheproofofTheorem3.2.
Given:isatransversal.
Prove:1and 2aresupplementary;
3and 4aresupplementary.
Proof:
ANSWER:
eSolutionsManual-PoweredbyCogneroPage1
3-2AnglesandParallelLines
pf3
pf4

Partial preview of the text

Download Angles and Parallel Lines: Finding Relationships and Solving Problems and more Lecture notes Reasoning in PDF only on Docsity!

Find the value of the variable(s) in each figure. Explain your reasoning.

ANSWER: y = 114 by the Corresponding Angles Postulate; x = 54 by the Supplement Theorem

ANSWER: x = 63 by the Vertical Angle Theorem and the Consecutive Interior Angles Theorem

ANSWER: x = 54 by the Alternate Interior Angles Theorem; y = 12 by the Consecutive Interior Angles Theorem

  1. PROOF Copy and complete the proof of Theorem 3.2. Given: is a transversal. Prove: 1 and 2 are supplementary; 3 and 4 are supplementary. Proof: ANSWER:

STORAGE When industrial shelving needs to be accessible from either side, additional support is provided on the side by transverse members. Determine the relationship between each pair of angles and explain your reasoning.

  1. 1 and 5 ANSWER: Congruent; Corresponding angles
  2. 1 and 2 ANSWER: Complementary; because the vertical and horizontal lines are perpendicular, they form right angles.
  1. REASONING Determine the minimum number of angle measures you would have to know to find the measures of all the angles formed by two parallel lines cut by a transversal. Explain. ANSWER: One; sample answer: Once the measure of one angle is known, the rest of the angles are either congruent or supplementary to the given angle.