Question

(1) Complete the proof of the following theorem.
Theorem: The corresponding angles
fromed by a transversal of two parallel
lines are of equal measure.
Given : line L parallel line m
line n is a transversal
To prove: angle a= angle b
Proof : angle a+angle c=.........(I) (angles in linear pair)
Angle b+angle c=........ (Il) (property of interior angles of parallel lines)
angle a + angle c = ............ + angle c-> (from (I) & (II))
ans. angle a..........
​

Answer 1

Answer:

Step-by-step explanation:

Consider line l and a point P that is not on line l. How many lines exist that are parallel to l and pass through point P?

 

[Figure1]

Line and Angle Theorems

Consider two parallel lines that are intersected by a third line. (Remember that tick marks (≫) can be used to indicate that two lines are parallel.)

 

[Figure2]

This third line is called a transversal. Note that four angles are created where the transversal intersects each line. Each angle created by the transversal and the top line has a corresponding angle with an angle create by the transversal and the bottom line. These corresponding angle pairs are shown color-coded below. How do you think these corresponding angles are related?

 

[Figure3]

Your intuition and knowledge of translations might suggest that these angles are congruent. Imagine translating one of the angles along the transversal until it meets the second parallel line. It will match its corresponding angle exactly. This is known as the corresponding angle postulate:

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

Remember that a postulate is a statement that is accepted as true without proof. Your knowledge of translations should convince you that this postulate is true.