Vocabulary Review&

Special Angles Created When Parallel Lines are Cut by a Transversal

with Ms. Evans & Ms. Straka Parallel Lines Cut by a Transversal – Part A

https://www.youtube.com/watch?v=w6PVwdJXhdk

Parallel Lines Cut by a Transversal – Part Bhttps://www.youtube.com/watch?v=Cl81BvbjRMg

Parallel Lines Cut by a Transversal - Part A & Bhttps://www.youtube.com/watch?v=LxIiUUJrsrY

Vocabulary Review

An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees.

One degree, or 1°, is of a circle.

m1 means the “measure of 1”.

An angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter.

1360

X

Y Z1 m1 = 50°

Angle Review

The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.

F K J

G H

The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.

P

R QM

N

Acute Angles – measure less than 90 degrees.

• <FKG is acute.

Obtuse Angles – measure more than 90 degrees.

• <GKJ is obtuse.

F K J

G H

A right angle can be labeled with a small box at the vertex.

Reading Math

A right angle measures 90°.

1st & 2nd Tabs in Vocab Flip Book

The notes that follow match the guided notes provided in the Parallel Lines Cut by a Transversal Vocabulary Flip Book, which was given in class.  • Fill in the blanks.       EX:  Right angles measure 90 degrees.

• Draw a picture in the block on the left or     right of the notes.  

• We will complete the folding, cutting, and     gluing of the Vocabulary Flip Book     in class.  

Complementary angles: Angles whose measures sum to 90°. A right angle measures 90°.

Angle symbol∡Supplementary angles: Angles whose measures sum to 180°. A straight line measures 180°.

A. Name a pair of complementary angles.

TQP, RQS mTQP + m RQS = 47° + 43° = 90°

Example: Classifying Angles

Example: Classifying Angles

B. Name two pairs of supplementary angles.

TQP, RQT mTQP + m RQT = 47° + 133° = 180°

3rd Tab in Vocab Flip Book

Vertical Angles: Angles formed by 2 intersecting lines. Vertical angles are always congruent.

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

Congruent Symbol: ≅

Example: Finding the Measure of Vertical Angles

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m1 = 37°, find m 3.

1 and 3 are vertical angles.

m3 = 37°

4th Tab in Vocab Flip Book

Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks.

The symbol for parallel is ||.

The railroad ties are transversals to the tracks.

A transversal is a line that intersects 2 or more lines in the same plane.

It creates angles with special properties when it intersects parallel lines.

The tracks are parallel.

Example: Identifying Congruent Angles Formed by a Transversal

Look at the angles formed by the transversal and parallel lines. Which angles seem to be congruent?

1, 3, 5, and 7 all measure 150°.

2, 4, 6, and 8 all measure 30°.

Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other.

1 @ 3 @ 5 @ 72 @ 4 @ 6 @ 8

13

57

24

68

Example Continued

5th Tab in Vocab Flip Book

Perpendicular lines: Lines that intersect at 90° angles.

The symbol for perpendicular is .

Coincidental Lines are the same line.

6th Tab in Vocab Flip Book

Alternate interior angles: 2 angleson opposite sides of the transversal and inside the parallel lines. These angles are ≌.

The pair of blue and the pair of pink angles are alternate interior angles.

7th Tab in Vocab Flip Book

Alternate exterior angles: 2 angleson opposite sides of the transversal and outside the parallel lines. These angles are ≌.

The pair of blue and the pair of pink angles are alternate exterior angles.

8th Tab in Vocab Flip Book

Corresponding angles: Angles in matching corners when 2 parallel lines are crossed by a transversal. Corresponding angles are ≌.

The pair of pink angles are corresponding. The pair of purple angles are corresponding. The blue pairs and green pairs are also corresponding.

Other Angles

Same side interior or consecutive interior angles are 2 angles inside the 2 parallel lines along the same side of a transversal line. These angles are supplementary.

1 23 4

5 67 8

Ex: <3 and <5 are same side interior angles. <4 and <6 are same side interior angles.

Same side exterior or consecutive exterior angles are 2 angles outside the 2 parallel lines along the same side of a transversal line. These angles are supplementary.

Ex: <1 and <7 are same side exterior angles. <2 and <8 are same side exterior angles.

1 23 4

5 67 8

Properties of 2 Parallel Lines Cut by a

Transversal

PROPERTIES OF TRANSVERSALS TO PARALLEL LINES

If two parallel lines are intersected by a transversal, • the acute angles that are formed are all congruent,• the obtuse angles are all congruent,• and any acute angle is supplementary to any obtuse angle.If the transversal is perpendicular to the parallel lines, all angles are 90°.

Add the notes below to your OMG.

In the figure, line l (L) || line m. Find the measure of the angle

Example: Finding Angle Measures of Parallel Lines Cut by Transversals

4.

m4 = 124°

All obtuse angles in the figure are congruent.

Example: Finding Angle Measures of Parallel Lines Cut by Transversals Continued

2.

m2 + 124° = 180°

2 is supplementary to the angle 124°.

m2 = 56°–124° –124°

In the figure, line l || line m. Find the measure of the angle