 Find the missing angles using properties of parallel lines cut

By Reynand Maitem

Simple Recall/Review

By Reynand Maitem

Direction: State the Postulate or Theorem that justify each statement. Choose the correct answer.

Poll

State the Postulate or Theorem that justify each statement.

$$\angle1\ and\ \angle5$$

• Same side exterior angle

• Corresponding angle

• Same side interior angle

• Linear Pair

Poll

State the Postulate or Theorem that justify each statement.

$$\angle1\ and\ \angle7$$

• Same side interior angle

• Alternate Exterior angle

• Corresponding angle

• Same side exterior angle

Poll

State the Postulate or Theorem that justify each statement.

$$\angle3\ and\ \angle5$$

• Same side interior angle

• Alternate Exterior angle

• Alternate interior angle

• Same side exterior angle

Poll

State the Postulate or Theorem that justify each statement.

$$\angle1\ and\ \angle3$$

• Corresponding angle

• Vertical angle

• Linear pair

• Same side exterior angle

Poll

State the Postulate or Theorem that justify each statement.

$$\angle6\ and\ \angle7$$

• Corresponding angle

• Vertical angle

• Linear pair

• Same side exterior angle

​Activity

TASK:
1. Draw two parallel lines. Label the first line as line l and the second
line as line m. Then draw a diagonal line intersecting the two lines
and name it as line t.
2. Label all the angles from 1 to 8.
3. Using a protractor, measure the angles.
4. list all pairs of corresponding, alternate interior, alternate exterior,
same side interior and same side exterior angles.
5. Observe the measurements and make conjectures about the
measures of the angle pairs.

​Analysis

1. What have you observed with the corresponding
angles?
2. How about the measurement of alternate interior
angles? Alternate exterior angles?
3. What did you notice with the side exterior angles?
Same side interior angles?
4. Just in case there is a missing measurement/s of an angle formed by parallel lines cut by a transversal, what steps should we take to find those missing angle/s?

Learning Objectives

By Reynand Maitem

• ​Find the missing angles using properties of parallel lines cut by transversal.

• Appreciate the importance of the concepts of parallel lines cut by transversal in real life situations.

Parallel line cut by a transversal have various applications to real life. In fact, you can see these lines all over the world.

PHYSICAL EDUCATION:
Using angles and lines to strategize movements and plays in sports.

SCIENCE:
Understanding angles and lines helps in explaining the reflection and refraction of light.

Interconnected of Knowledge in various subjects:

TLE:
Knowledge of parallel lines and transversal is essential in creating accurate technical drawing and blueprints.

ARTS:
Applying the properties of parallel lines and transversals in perspective drawing to create realistic artworks.

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Now, look around you and cite example that illustrate parallel lines cut by a transversal.

When the lines are parallel to each other and is cut by a transversal, then
1. Corresponding angles are congruent.
2. Alternate-interior angles are congruent.
3. Alternate-exterior angles are congruent.
4. Interior angles on the same side of the transversal are supplementary.
5. Exterior angles on the same side of the transversal are supplementary.


to find the measure of the different angles, use these theorems/postulates.

Illustrative Example

Illustrative Example

The figure below shows road map in Maasin City. The College of Maasin and Jollibee Maasin Branch are Parallel lines cut by transversal. Use the satellite photo and the given information to
determine the values x and
each angle.

 
 
 
 

Application

​Group 1: Maasin City Cathedral

​Group 2: Pering-Chaibio Building

​Group 3: Anatalio Gaviola Plaza

​Group 4: J & F Department Store Building

​By Group:
Determine the value of x and measure of each angle.
How do you know? State your reasons?

Assessment

Direction: Read and analyze each statement carefully. Applies properties of parallel lines cut by transversal in finding the missing angles. Choose the correct answer.

Multiple Choice

Given $$a\parallel b$$ with transversal t.

What is the measure of $$\angle5$$ if the measure of $$\angle7=70?$$

• 100

• 80

• 70

• 110

Multiple Choice

Given: $$\angle1=3x-4$$ ; $$\angle3=5x-38$$

Find the measure of $$\angle4$$ .

• 44

• 136

• 16

• 164

Multiple Choice

Given the two parallel lines cut by a transversal, what is the measure of $$\angle4$$ if $$m\angle8=76^{\circ}$$ ?

• 104

• 67

• 140

• 76

Multiple Choice

if $$m\angle RNP=\left(8x+63\right)^{\circ}$$ and $$m\angle NRS=5x^{\circ}$$ ,

find $$m\angle RNP.$$

• 117

• 45

• 135

• 9

Multiple Choice

What is the value of x?

• 6

• 10

• 14

• 18

Assignment

Reflection Journal (1 whole A4 Bond paper)
The ladder is an example of parallel lines cut by transversal. If the ladder serves as your success in life, you cannot climb it if you do not exert your best effort to accomplish it. As a student, how do you climb your ladder of success and cite ways how you can accomplish it.