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draw two lines and a transversal such that ∠1 and ∠2 are alternate interior angles, ∠2 and ∠3 are corresponding angles, and ∠3 and ∠4 are alternate exterior angles. what type of angle pair is ∠1 and ∠4?

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James

Guys, does anyone know the answer?

get draw two lines and a transversal such that ∠1 and ∠2 are alternate interior angles, ∠2 and ∠3 are corresponding angles, and ∠3 and ∠4 are alternate exterior angles. what type of angle pair is ∠1 and ∠4? from EN Bilgi.

Angles and Parallel Lines

Angles and Parallel Lines MathBitsNotebook.com

Topical Outline | Geometry Outline | MathBits' Teacher Resources

When a transversal intersects two or more lines in the same plane, a series of angles are formed. Certain pairs of angles are given specific "names" based upon their locations in relation to the lines. These specific names may be used whether the lines involved are parallel or not parallel.

"Names" given to pairs of angles:

• alternate interior angles

• alternate exterior angles

• corresponding angles

• interior angles on the same side of the transversal

Let's examine these pairs of angles in relation to parallel lines:

Alternate Interior Angles:The word "alternate" means "alternating sides" of the transversal.

This name clearly describes the "location" of these angles.

When the lines are parallel,

the measures are equal.

∠1 and ∠2 are alternate interior angles

∠3 and ∠4 are alternate interior angles

Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (next to one another sharing a vertex).

When the lines are parallel,

the alternate interior angles

are equal in measure.

m∠1 = m∠2 and m∠3 = m∠4

If you draw a Z on the diagram, the alternate interior angles can be found in the corners of the Z. The Z may also be backward:.

If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

Converse

If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.

Alternate Exterior Angles:The word "alternate" means "alternating sides" of the transversal.

The name clearly describes the "location" of these angles.

When the lines are parallel, the measures are equal.

∠1 and ∠2 are alternate exterior angles

∠3 and ∠4 are alternate exterior angles

Alternate exterior angles are "exterior" (outside the parallel lines), and they "alternate" sides of the transversal. Notice that, like the alternate interior angles, these angles are not adjacent.

When the lines are parallel,

the alternate exterior angles

are equal in measure.

m∠1 = m∠2 and m∠3 = m∠4

If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

Converse

If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel.

Corresponding Angles: The name does not clearly describe the "location" of these angles. The angles are on the SAME SIDE of the transversal, one INTERIOR and one EXTERIOR, but not adjacent.

The angles lie on the same side of the transversal in "corresponding" positions.

When the lines are parallel,

the measures are equal.

∠1 and ∠2 are corresponding angles

∠3 and ∠4 are corresponding angles

∠5 and ∠6 are corresponding angles

∠7 and ∠8 are corresponding angles

If you copy one of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle. For example, slide ∠ 1 down the transversal and it will coincide with ∠2.

When the lines are parallel,

the corresponding angles

are equal in measure.

m∠1 = m∠2 and m∠3 = m∠4

m∠5 = m∠6 and m∠7 = m∠8

If you draw a F on the diagram, the corresponding angles can be found in the corners of the F. The F may also be backward and/or upside-down: .

If two parallel lines are cut by a transversal, the corresponding angles are congruent.

Converse

If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

Source : mathbitsnotebook.com

Transversal

In geometry, a transversal is a line that intersects two or more other (often parallel) lines. In the figure below, line n is a transversal cutting lines l and m.

Transversal

In geometry, a  transversal  is a line that intersects two or more other (often  parallel ) lines.

In the figure below, line

n n

is a transversal cutting lines

l l and m m .

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

In the figure the pairs of corresponding angles are:

∠1 and ∠5 ∠2 and ∠6 ∠3 and ∠7 ∠4 and ∠8

∠1 and ∠5∠2 and ∠6∠3 and ∠7∠4 and ∠8

When the lines are parallel, the corresponding angles are congruent .

When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .

In the above figure, the consecutive interior angles are:

∠3 and ∠6 ∠4 and ∠5 ∠3 and ∠6∠4 and ∠5

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary .

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .

In the above figure, the alternate interior angles are:

∠3 and ∠5 ∠4 and ∠6 ∠3 and ∠5∠4 and ∠6

If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .

In the above figure, the alternate exterior angles are:

∠2 and ∠8 ∠1 and ∠7 ∠2 and ∠8∠1 and ∠7

If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent .

Example 1:

In the above diagram, the lines

j j and k k

are cut by the transversal

l l . The angles ∠c ∠c and ∠e ∠e are…

A. Corresponding Angles

B. Consecutive Interior Angles

C. Alternate Interior Angles

D. Alternate Exterior Angles

The angles ∠c ∠c and ∠e ∠e

lie on either side of the transversal

l l

and inside the two lines

j j and k k .

Therefore, they are alternate interior angles.

The correct choice is

C C .

Example 2:

In the above figure if lines

AB ← → AB↔ and CD ← → CD↔ are parallel and m∠AXF=140° m∠AXF=140°

then what is the measure of

∠CYE ∠CYE ? The angles ∠AXF ∠AXF and ∠CYE ∠CYE

lie on one side of the transversal

EF ← → EF↔

and inside the two lines

AB ← → AB↔ and CD ← → CD↔

. So, they are consecutive interior angles.

Since the lines AB ← → AB↔ and CD ← → CD↔

are parallel, by the consecutive interior angles theorem ,

∠AXF ∠AXF and ∠CYE ∠CYE are supplementary. That is, m∠AXF+m∠CYE=180° m∠AXF+m∠CYE=180° . But, m∠AXF=140° m∠AXF=140° .

Substitute and solve.

140°+m∠CYE=180°

140°+m∠CYE−140°=180°−140°

m∠CYE=40°

140°+m∠CYE=180°140°+m∠CYE−140°=180°−140°m∠CYE=40°

Source : www.varsitytutors.com

Draw two lines and a transversal such that $\angle \mathbf { Find step-by-step Geometry solutions and your answer to the following textbook question: Draw two lines and a transversal such that$\angle \mathbf { 1 }$and$\angle \mathbf { 3 }$are corresponding angles.$\angle \mathbf { 1 }$and$\angle \mathbf { 2 }$are alternate interior angles, and$\angle \mathbf { 3 }$and$\angle \mathbf { 4 }$are alternate exterior angles. What type of angle pair is$\angle \mathbf { 2 }$and$\angle \mathbf { 4 }\$?.

Question

Draw two lines and a transversal such that

\angle \mathbf { 1 }

∠1 and

\angle \mathbf { 3 }

∠3 are corresponding angles.

\angle \mathbf { 1 }

∠1 and

\angle \mathbf { 2 }

∠2 are alternate interior angles, and

\angle \mathbf { 3 }

∠3 and

\angle \mathbf { 4 }

∠4 are alternate exterior angles. What type of angle pair is

\angle \mathbf { 2 }

∠2 and

\angle \mathbf { 4 }

∠4?

Verified

Related questions

GEOMETRY

Draw two lines and a transversal such that

\angle 1 ∠1 and \angle 3

∠3 are corresponding angles,

\angle 1 ∠1 and \angle 2

∠2 are alternate interior angles, and

\angle 3 ∠3 and \angle 4

∠4 are alternate exterior angles. What type of angle pair is

\angle 2 ∠2 and \angle 4? ∠4? ALGEBRA

Draw two parallel lines and a transversal intersecting both.

PREALGEBRA

Suppose a transversal intersects two parallel lines. One angle that is formed is a right angle. What are the measures of the remaining angles? What is the relationship between the transversal and the parallel lines?

PREALGEBRA

Draw two parallel lines and a transversal. Label a pair of corresponding angles.

Source : quizlet.com

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James 9 month ago

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