Geometry Student Text 2nd Edition Chapter 2 Parallel and Perpendicular Lines
Carnegie Learning Geometry Student Text 2nd Edition Chapter 2 Exercise 2.2 Solution Page 87 Problem 1 Answer
Given:
To identify: The corresponding angles.
The pair of corresponding angles are
∠1=∠3
∠2=∠4
∠5=∠7
∠6=∠8
The pair of corresponding angles are
∠1=∠3
∠2=∠4
∠5=∠7
∠6=∠8
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Page 88 Problem 2 Answer
Page 88 Problem 3 Answer
Given:
To write: The conjecture about the alternate exterior angles.
The pair of alternate exterior angles are congruent.
∠8=∠6
As they are corresponding angles.
∠1=∠6
As they are vertically opposite angles.
It can be said that:∠1=∠8
The pair of alternate exterior angles are congruent.
Solutions For Parallel And Perpendicular Lines Exercise 2.2 In Carnegie Learning Geometry Page 88 Problem 4 Answer
Given:
To write: A conjecture for same side angles and prove it.
The same side interior angles are supplementary.
The proof is ∠1+∠2=180∘
∠3+∠4=180∘
They are linear pair angles.
As the corresponding angles are equal:
∠1=∠3
∠2=∠4
Substituting the values we can say that:
∠3+∠2=180∘
∠2+∠3=180∘
Adding the equations: 2(∠2+∠3)=360∘
∠2+∠3=180∘
The same side interior angles are supplementary.
Page 88 Problem 5 Answer
Given:
To write: A conjecture about the dame side exterior angles.
The same side exterior angles are supplementary.
Proof: ∠1+∠2=180∘
∠3+∠4=180∘
They are linear pair angles.
Adding the equations: ∠1+∠2+∠3+∠4=360∘
∠2+∠3=180∘
As they are the same side interior angles.
∠1+∠4=180∘
The same side exterior angles are supplementary.
Carnegie Learning Geometry 2nd Edition Exercise 2.2 Solutions Page 88 Problem 6 Answer
To find: Whether the conjectures are inductive or deductive.
The conjectures are inductive as we have the data and we wrote the conjectures.
The conjectures are inductive as we have the data and we wrote the conjectures.
Page 89 Problem 7 Answer
Given: Two parallel lines and transversal, m∠1=38∘
To find: All unknown angles.
m∠1=m∠6=38∘
As they are vertically opposite angles.
38∘+∠2=180∘
∠2=142∘
∠2=∠5=142∘
As they are vertically opposite angles.
∠7=∠5=142∘
As they are corresponding angles
∠7=∠4=142∘
As they are vertically opposite angles.
m∠1=m∠3=38∘
As they are corresponding angles
m∠8=m∠3=38∘
As they are vertically opposite angles.
∠1 = 38∘
∠2 = 142∘
∠3 = 38∘
∠4 = 142∘
∠5 = 142∘
∠6 = 38∘
∠7 = 142∘
∠8 = 38∘
Parallel And Perpendicular Lines Solutions Chapter 2 Exercise 2.2 Carnegie Learning Geometry Page 89 Problem 8 Answer
Given: ∠1=67∘
To find: The unknown angles.
∠1=∠6=67∘
As they are vertically opposite angles.
As the corresponding angles are equal: ∠1=∠3=67∘
∠6=∠8=67∘
Linear pair angles: ∠1+∠2=180∘
∠2=113∘
Vertically opposite angles: ∠2=∠5=113∘
As the corresponding angles are equal: ∠2=∠4=113∘
Vertically opposite angles: ∠7=∠4=113∘
∠1=67∘
∠2=113∘
∠3=67∘
∠4=113∘
∠5=113∘
∠6=67∘
∠7=113∘
∠8=67∘
Step-By-Step Solutions For Carnegie Learning Geometry Chapter 2 Exercise 2.2 Page 90 Problem 9 Answer
Explain the Alternate Interior Angle Conjecture.
The Alternate Interior Angle Conjecture states that the alternate interior angles are congruent if the set of parallel lines are cut by a transversal line.
The Alternate Interior Angle Conjecture states that the alternate interior angles are congruent if the set of parallel lines are cut by a transversal line.
Page 90 Problem 10 Answer
Explain the Alternate Exterior Angle Conjecture.
The Alternate Exterior Angle Conjecture states that the alternate exterior angles are congruent when the set of parallel lines are intersected by a transversal line.
The Alternate Exterior Angle Conjecture states that the alternate exterior angles are congruent when the set of parallel lines are intersected by a transversal line.
Carnegie Learning Geometry Chapter 2 Exercise 2.2 Free Solutions Page 90 Problem 11 Answer
Explain the Same-Side Interior Angle Conjecture.
The Same-Side Interior Angle Conjecture states that the same side interior angles are supplementary if the set of parallel lines are cut by a transversal line.
The Same-Side Interior Angle Conjecture states that the same side interior angles are supplementary if the set of parallel lines are cut by a transversal line.
Carnegie Learning Geometry Exercise 2.2 Student Solutions Page 90 Problem 12 Answer
Explain the Same-Side Exterior Angle Conjecture.
The Same-Side Exterior Angle Conjecture states that the same side exterior angles are supplementary if the set of parallel lines are cut by a transversal line.
The Same-Side Exterior Angle Conjecture states that the same side exterior angles are supplementary if the set of parallel lines are cut by a transversal line.